# Wood Species Recognition Based on Visible and Near-Infrared Spectral Analysis Using Fuzzy Reasoning and Decision-Level Fusion

Authors: Peng Zhao; Zhen-Yu Li; Cheng-Kun Wang
Journal: Journal of Spectroscopy
 (2021)

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## Abstract

A novel wood species spectral classification scheme is proposed based on a fuzzy rule classifier. The visible/near-infrared (VIS/NIR) spectral reflectance curve of a wood sample’s cross section was captured using a USB 2000-VIS-NIR spectrometer and a FLAME-NIR spectrometer. First, the wood spectral curve—with spectral bands of 376.64–779.84 nm and 950–1650 nm—was processed using the principal component analysis (PCA) dimension reduction algorithm. The wood spectral data were divided into two datasets, namely, training and testing sets. The training set was used to generate the membership functions and the initial fuzzy rule set, with the fuzzy rule being adjusted to supplement and refine the classification rules to form a perfect fuzzy rule set. Second, a fuzzy classifier was applied to the VIS and NIR bands. An improved decision-level fusion scheme based on the Dempster–Shafer (D-S) evidential theory was proposed to further improve the accuracy of wood species recognition. The test results using the testing set indicated that the overall recognition accuracy (ORA) of our scheme reached 94.76% for 50 wood species, which is superior to that of conventional classification algorithms and recent state-of-the-art wood species classification schemes. This method can rapidly achieve good recognition results, especially using small datasets, owing to its low computational time and space complexity.


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## Body

## 1. Introduction

Wood species classification has been investigated for several years, as different wood species have diverse physical and chemical properties. Many such schemes have been proposed for automatic processing using sensors and computers, with spectra-based [1–3], chemometric-based [4], and image-based schemes [5–9] being the most commonly investigated. Spectral analysis technology is also widely used in the prediction of wood properties [10–12] such as wood density [13], wood moisture content [14, 15], and others [16, 17]. The NIR spectral band is often used in these applications. A wood spectral analysis scheme usually pertains to one-dimensional (1D) spectral reflectance curves, which exhibits low computational complexity and, thus, high processing speeds. A wood image processing scheme usually considers the wood’s texture features for species classification, as its texture is more stable than its color [18–20].Fuzzy logic can provide nonseparated output classes and functions well with just a few learning datasets. In the past, fuzzy-rule-based schemes were successfully used in control systems and pattern recognition applications [21, 22]. In the wood industry, fuzzy rule classification has been successfully applied to wood color classification and wood defect recognition [23–25]. For example, considering the uncertainty of wood color and processing speed, Bombardier et al. proposed a fuzzy rule classifier to fulfill wood color recognition [24, 25].Fuzzy rule classification is not frequently used in wood species recognition. However, Ibrahim et al. proposed a fuzzy preclassifier to classify 48 tropical wood species into four broad categories, followed by the use of a support vector machine (SVM) classifier in each broad category to further determine the wood species of a sample [19]. One advantage of their approach was that when a new wood species was added to the system, only the SVM classifier of one broad category required retraining instead of the entire system. Similarly, Yusof et al. also proposed a fuzzy-logic-based preclassifier to classify tropical wood species into four broad categories, followed by performing specific wood species recognition using definite classifiers to increase recognition accuracy and decrease processing time requirements [7].In this study, we propose a fuzzy rule classification scheme for the recognition of 50 wood species using 1D spectral reflectance data. The spectral range covers both the visible (VIS) band (i.e., 376.64–779.84 nm) and the near-infrared (NIR) band (i.e., 950–1650 nm). For the wood spectral curves, the VIS band may vary as the color of a wood sample may change owing to environmental variations, while the NIR band remains relatively stable. Consequently, these two bands were processed using different fuzzy classifiers, and the two classification results were further processed using an improved decision-level fusion based on the D-S evidential theory.Our scheme has the two following advantages. First, it can achieve good recognition accuracy rapidly in a small spectral dataset. There are only 50 samples for each wood species, and each sample consists of a VIS spectral curve and an NIR curve. Second, the experimental equipment cost is low. The used Ocean Optics USB2000-VIS-NIR spectrometer costs approximately $3,000, while the Ocean Optics FLAME-NIR spectrometer costs $8,000. Several comparisons with other classical and state-of-the-art classifiers in wood species recognition also verified the merits of our scheme.


## 2. Materials and Methods

### 2.1. Wood Samples and Spectral Data Acquisition

Our wood dataset consists of 50 wood species, as shown in Table1 and Figure 1. These 50 wood species consist of softwood and hardwood species, which are representative tree species in the wood market. Moreover, this dataset also consists of some similar wood species (i.e., visually similar wood species and intragenus different species). Each wood sample was processed into a 2 × 2 × 3 cm block. We used the Ocean Optics USB2000-VIS-NIR microfiber spectrometer and an Ocean Optics FLAME-NIR microfiber spectrometer, visible and near-infrared (VIS/NIR) spectra of the wood samples being obtained using these devices. Fifty mean spectral curves were detected by using the spectrometer for each wood species—that is, there are 2500 VIS spectral curves and 2500 NIR spectral curves for 50 wood species. Our experimental setup consisted of a halogen lamp, a universal serial bus, a computer, a customized holder, a fiber spectrometer, and a section of optical fiber, as shown in Figure 2. Spectral acquisition was performed in a controlled environment at a temperature interval of 20±2°C. The VIS spectral band covered a range of 376.64–779.84 nm, with a spectral resolution of approximately 0.3 nm. The NIR spectral band covered a range of 950–1650 nm, with a spectral resolution of approximately 5.4 nm. The spectrometer parameter settings, spectral data acquisition, and data storage were conducted using the Spectrasuite software. The integration time was 300 ms, and the mean number of measurements at each point was 900. Before spectral acquisition, the reference and dark spectra were measured and stored, the reference spectra were acquired using a standard white panel of known 100% reflectance, and the dark spectra were acquired by blocking the radians. For each wood sample, four diffuse reflectance spectra were measured randomly using (1)—where IR,IB,andIW represented the received intensity, dark intensity, and white panel intensity, respectively—at different locations across the wood sample’s cross section. In fact, wood cross section has plentiful wood structures such as pores and parenchyma, making its spectra more suitable for species recognition, which is superior to radial direction and tangential direction in wood species recognition [26] and wood density prediction [13]. Subsequently, the mean spectrum of each wood sample was calculated and stored for subsequent spectral analysis and species classification. Figures 3 and 4 show the acquired mean spectra of the 50 wood species with standard normal variables (SNVs).(1)ref=IR−IBIW−IB.Table 1
The names of the wood species.
Class labelLatin name1Pterocarpus soyauxii2Ulmus glabra3Calophyllum brasiliense4Intsia bijuga5Tectona grandis6Pouteria speciosa7Quercus mongolica8Magnolia fordiana9Guibourtia ehie10Terninalia catappa11Cinnamomum camphora12Guibourtia demeusei13Swintonia florbunda14Fraxinus mandshurica15Pometia pinnata16Dipterocarpus alatus17Vernicia fordii18Sophora japonica19Robinia pseudoacacia20Quercus acutissima21Populus alba22Fraxinus chinensis23Pinus sylvestris24Populus tomentosa25Betula alnoides26Betula platyphylla27Platanus orientalis28Picea asperata29Larix gmelinii30Salix matsudana31Amygdalus davidiana32Juglans mandshurica33Pinus koraiensis34Populus cathayana35Tona ciliate36Prunus avium37Pinus massoniana38Aucoumea klaineana39Shorea contorta40Entandrophragma candollei41Millettia laurentii42Swietenia mahagoni43Rhodamnia dumetorum44Cyclobalanopsis glauca45Shorea laevis46Chamaecyparis nootkatensis47Juglans nigra48Tilia mandshurica49Pseudotsuga menziesii50Pinups radiataFigure 1
Wood samples for 50 wood species, and the order is the same as that in Table1 (see Table 1 for specific wood species names).Figure 2
Our spectral acquisition system.Figure 3
VIS spectral reflectance curves for 50 wood species with SNV.Figure 4
NIR spectral reflectance curves for 50 wood species with SNV.The spectral range of the USB2000-VIS-NIR spectrometer was 340–1027 nm. Both ends of this spectral range can be noisy, so the useful spectral range is 376.64–779.84 nm. The spectral data in the VIS band may be variable as the color of a wood sample may change with changing environmental conditions. To avoid this, we maintained a stable environment during spectral acquisition and wood sample preservation. The NIR band of 950–1650 nm is relatively stable and can be used to characterize different wood properties to some extent. Therefore, these two bands were processed using different fuzzy classifiers—that is, with different membership functions and fuzzy rules—the two classification results of which were further processed using an improved decision-level fusion based on the D-S evidential theory.


### 2.2. Spectral Dimension Reduction

For each spectral curve, the VIS/NIR band includes thousands of spectral data, so that the spectral dimension is very large. Consequently, each spectral curve contains redundant information, which reduces the wood species classification accuracy and speed. We used principal component analysis (PCA) and the T-distributed stochastic neighbor embedding (T-SNE) algorithms to compare and reduce the spectral dimension results. The PCA algorithm is a transformation algorithm in multivariate statistics, which is based on the variance maximization of a mapped low-dimension vector. The procedure is as follows: First, the initial dataset matrix is defined asAm×n=a1,…,an—where m and n are the dimension and number of feature vectors, respectively. The mean vector is computed as u=1/n∑i=1nai. Second, we compute xi=ai−u to form Xm×n=x1,…,xn. Third, the k largest eigenvalues of XXT are selected, their k corresponding eigenvectors ε1,…,εk forming a matrix D=ε1,…,εk. Finally, the new dataset matrix after dimension reduction is computed as DT×X=Pk×nk<m.Additionally, the T-SNE algorithm was also used for spectral dimension reduction. This algorithm performs nonlinear dimension reduction, an improvement on the original SNE algorithm [27]. The algorithm is based on the invariant data distribution probability of the mapped low-dimensional vector. Here, the symbol “T” in T-SNE represents the t-distribution, the freedom of the t-distribution being 1 in this study. The graphs of the three-dimensional (3D) spectral vectors for the VIS and NIR bands after spectral dimension reduction using the PCA and T-SNE algorithms are shown in Figure 5. The contribution rate (CR) and cumulative contribution rate (CCR) of the first ten principal components are shown in Figure 6 and Table 2 for the VIS and NIR bands. In Figure 5, the wood sample’s 3D spectral vectors were acquired using the PCA and T-SNE algorithms and are shown with 50 different colors for the 50 wood species. The best case is shown in Figure 5(b), where the wood samples were the most dispersed.Figure 5
Spectral dimension reduction 3D results: (a) PCA for the VIS band; (b) PCA for the NIR band; (c) T-SNE for the VIS band; and (d) T-SNE for the NIR band.
(a)(b)(c)(d)Figure 6
Contribution of PC by using PCA: (a) contribution rate of PC for the VIS band; (b) cumulative contribution rate of PC for the VIS band; (c) contribution rate of PC for the NIR band; and (d) cumulative contribution rate of PC for the NIR band.
(a)(b)(c)(d)Table 2
The contribution rate (CR) and cumulative contribution rate (CCR) of the principal components (PCs) for visible (VIS) and near-infrared (NIR) spectral data.
PC01PC02PC03PC04PC05PC06PC07PC08PC09PC10VIS CR0.88040.07260.03010.00700.00610.00180.000749820.000559080.000478820.00027888VIS CCR0.88040.95290.98300.99000.99610.99790.99860.99920.99970.9999NIR CR0.82150.14680.01550.00970.00290.00210.000823300.000230930.000173110.00010637NIR CCR0.82150.96830.98380.99350.99650.99870.99940.99970.99980.9999


### 2.3. Fuzzy Rule Classifier

A fuzzy rule classifier is a fuzzy reasoning system based on fuzzy linguistic rules, its core component being a fuzzy rule set. When an input sample is transformed into the rule set of one wood species, this sample is then classified as a wood species. The overall fuzzy reasoning system is shown in Figure7 and consists of two parts: the training and testing processes. The steps in Figure 7 are presented as follows.Step 1. The membership functions are set to fuzzify the training sample’s feature and generate the training sample’s fuzzy rulesStep 2. Fuzzy rules are adjusted by using a corrected confidence coefficientStep 3. The fuzzy rule set is generatedStep 4. The testing sample’s feature is fuzzified, and the generated rule is compared with the fuzzy rule set for wood species classificationFigure 7
Workflow graph of our fuzzy rule classification system.The training process consisted of three steps. First, membership functions were used to fulfill the fuzzification of the training dataset. Here, the membership functions could be a triangular function, trapezoid function, or Gaussian function. Second, fuzzy rules were generated based on the wood species of the wood samples in the training dataset. A fuzzy rule was defined as “IF … AND …, THEN …” using the conjunction or disjunction operation. Third, the fuzzy rules required modification using a confidence coefficient to form a perfect fuzzy rule set.In the testing process, the testing dataset was added to the trained fuzzy rule classifier, and the same membership functions were used to fulfill its fuzzification. In this way, a corresponding fuzzy rule of a testing sample could be obtained, and this rule was compared with the generated perfect fuzzy rule set to obtain the classified wood species. This species was then compared with the correctly labeled species of the testing sample to evaluate the performance of the fuzzy rule classifier. If the corresponding fuzzy rule of a testing sample was not found in the perfect fuzzy rule set, the sample was classified as an unknown species.


#### 2.3.1. Fuzzification of the Feature Vector

Here, the feature vector refers to the spectral vector after dimension reduction. This fuzzification step transforms spectral feature vectors into linguistic variables. A linguistic variable is defined using a triple valueV,X,TV, where V is a variable (e.g., PC1) defined on a set of reference X, X is the universe of discourse (field of variation of V), and TV is the vocabulary chosen to describe the values of V in a symbolic way. The set TV=A1,A2,… contains the normalized fuzzy subsets of X, and each fuzzy subset Ai is defined by the membership degree uAi.For example, the wood spectral feature vector is obtained using the PCA algorithm. The fourth principal component (PC4) of the first ten wood species is shown in Table3 for the NIR band, where the maximum, minimum, mean, and median values of PC4 are shown. Thus, we can design the membership functions to divide the NIR PC4 (i.e., the 4th dimension) into twenty-six intervals TV=A1,A2,…,A26 based on these values, as shown in Figure 8.Table 3
Principal component 4 (PC4) data for the first ten wood species in the near-infrared (NIR) band.
Wood speciesMinimum valueMean valueMedian valueMaximum valuePterocarpus soyauxii−0.292834701−0.16041152−0.1699747120.007724295Ulmus glabra0.0253157880.1957505660.2108186090.363952969Calophyllum brasiliense−0.192778352−0.117200877−0.117229875−0.034786326Intsia bijuga−0.389917083−0.139350711−0.1377726120.114471138Tectona grandis−0.0575578260.1481586360.1533149030.280022623Pouteria speciosa−0.0950309850.0538110880.0500285470.191835329Quercus mongolica−0.0629643380.0561465120.0465165520.338022639Magnolia fordiana−0.154656742−0.037434328−0.0481849820.126992175Guibourtia ehie−0.338868726−0.178740936−0.2012918660.085960311Terninalia catappa−0.1871783530.0607163560.0537035390.267102296Figure 8
PC4 is divided into 26 intervals by use of membership functions for the NIR band.As the different spectral PCs or dimensions may be divided into different intervals, the overall number of fuzzy rules is the product of the interval number of different PCs or dimensions:(2)Nrules=∏V=1NCardTV,where N is the dimension of the spectral feature vectors and CardTV is the number of intervals for variable V (i.e., the element of the spectral feature vector). In fact, Nrules can be determined by both N and CardTV. Therefore, a large N or CardTV produces a large Nrules resulting in high computational complexity. In other words, N and CardTV should be designed to be as small as possible in view of the recognition accuracy of our fuzzy rule classifier. If they cannot be simultaneously small, the dimension N should be as small as possible.For instance, if the PCA algorithm is used for wood spectral dimension reduction, the CCR should be above 99% in view of the PC number. As can be seen from Table2, the CCR of the first four PCs reaches 99% and 99.35% for the VIS and NIR bands, respectively, but remains approximately stable when N>4, so we should set N≥4.After several tests with the PCA algorithm,N and CardTV were as follows: for the VIS band, CardT1=37,CardT2=35,CardT3=25, CardT4=21,CardT5=15,and CardT6=2. For the NIR band, CardT1=47,CardT2=40,CardT3=28, CardT4=26,CardT5=20,and CardT6=2. The triangular, trapezoid, and triangular-trapezoid functions were used and compared 50 times—in terms of the ORA and mean training time requirement (i.e., the wood sample number of the training set was 2000) for the fuzzy rule set—as described in Tables 4 and 5 for the VIS and NIR bands, respectively. The maximum and practical Nrules in terms of N and CardTV are listed in Table 6. We observed that the training time requirement for the fuzzy rule set was practically invariant with regard to the fuzzy classifiers based on different membership functions. However, this time requirement was only relevant to the N dimension of the spectral feature vectors. In fact, both the time requirement and the Nrules increased rapidly when the dimension N increased. Moreover, the overall recognition accuracy in terms of the triangular-function-based fuzzy classifier increased when the dimension N increased, but the trapezoid-function- or triangular-trapezoid-function-based classifier remained practically invariant when the dimensions were N≥4 and N≥6 for the VIS and NIR bands, respectively. Finally, using our fuzzy classifier, the optimal trapezoid function parameters were dimension N=37, CardT1=35,CardT2=25,CardT3=25, and CardT4=21 for the VIS band and N=4,CardT1=47,CardT2=40,CardT3=28,and CardT4=26 for the NIR band.Table 4
Overall recognition accuracy (ORA) and training time requirement (TR) of differentN and membership functions in the visible (VIS) band.
DimensionNTriangular functionTrapezoid functionTriangular-trapezoidORA (%)TR (s)ORA (%)TR (s)ORA (%)TR (s)375.651051.2776.851154.1277.801219.26489.0524393.2489.6025128.7590.2024983.20589.60312764.5290.05299023.2090.25327279.92690.20556719.4790.40469466.5390.65483718.36Table 5
Overall recognition accuracy (ORA) and training time requirement (TR) of differentN and membership functions in the near-infrared (NIR) band.
DimensionNTriangular functionTrapezoid functionTriangular-trapezoidORA (%)TR (s)ORA (%)TR (s)ORA (%)TR (s)377.651822.2382.801733.4681.151807.12490.2545125.0292.9044783.2493.2548353.50591.55657271.1593.10631285.4692.85718375.61692.051038488.1893.05940615.3493.351223481.25Table 6
Maximum and practical fuzzy rule numbers.
DimensionN345(VIS) maximum fuzzy rule number4532595182514277375(VIS) practical fuzzy rule number98713621475(NIR) maximum fuzzy rule number52640136864027372800(NIR) practical fuzzy rule number113516741689


#### 2.3.2. Fuzzy Rule Generation

After the fuzzification of the spectral feature vectors, the fuzzy rules in the form of “IF … AND …, THEN …” required definition. For example, if three linguistic variables are considered for inputV1,V2,V3 and the output is wood species Y, the fuzzy rule is as follows:(3)IFV1isAIANDV2isBJANDV3isCKTHENYisClassl.This expression indicates that whenV1 is classified as AI, V2 is classified as BJ …, and the output class is Classl. Therefore, we need to calculate the membership degrees uAi,uBj,uCk for input V1,V2,V3. In this expression, “AND” is a Cartesian product between the linguistic variables and the operation is performed with a T-Norm, as follows:(4)Tx,y,z=x×y×z.This equation is then used to calculate the product of the membership degrees for the spectral linguistic variablesV1,V2,V3:(5)βClassls=uAi×uBj×uCk.For one wood sample of wood class/speciesl, there are often some products of the membership degrees βClassls≠0,s=1,2,…,S. For example, if uA1,uA3,uA4,uB1,uB5,uC1 are not equal to 0, we obtain 3×2×1=6 products of the membership degrees for one wood sample (i.e., βClassls,s=1,2,…,6). We should then choose the largest product to form the corresponding rule. Thus, we obtain a fuzzy rule for wood class/species l as follows:(6)maxβClassls=uAI×uBJ×uCK.


#### 2.3.3. Fuzzy Rule Adjustment

When the fuzzy rule is generated, there are usually several rules with the same judgment condition (i.e., the same “IF … AND …,”) but different classification results (i.e., different “THEN …”). Consequently, fuzzy rule adjustment is usually required to add a confidence coefficient (CC) to each fuzzy rule.First, for one wood sample of wood class/speciesl, the sum of the products of the membership degrees βClassls≠0,s=1,2,…,S is calculated as follows:(7)βsum=∑s=1SβClassls.Then, the mean value is calculated using(8)βmean=βsum−maxβClasslsS−1.Thus, we can compute the CC of the fuzzy rule produced as follows:(9)CC=maxβClassls−βmeanβsum.Moreover, when the same rules are produced by other samples, the CC of the fuzzy rule should be increased as follows:(10)CC=CC+α1−CC.If the same rule is not produced by other samples, the CC of this fuzzy rule remains invariant. Some final rules with their CCs are listed in Table7. In practical classification work, when there are rules that have the same judgment condition but different classification results, the final classification is determined by the fuzzy rule with the largest CC.Table 7
The fuzzy rule set with a confidence coefficient (CC) for the visible (VIS) band.
ABCDCCWood species224860.9939Pinups radiata5209150.9876Tilia mandshurica282920150.9072Juglans nigra………………1721260.7993Entandrophragma candollei3231160.6161Chamaecyparis nootkatensis………………


### 2.4. Decision-Level Fusion

The D-S evidential theory [28] is an effective decision-level fusion scheme, but the classifier’s reliability is not considered fully when each classifier’s result is converted into a classification probability distribution before the decision-level fusion. To solve this problem, we proposed an improved D-S decision-level fusion method that determines each classifier’s weight in view of the differences in the classification accuracy ratio and correlation coefficient.As the NIR band is more stable than the VIS band, these two bands should be processed using different fuzzy parameters (e.g., different membership functions). Consequently, spectral dimension reduction and fuzzy rule classification were applied to the two bands, respectively, so that the two classification results could be fused with our improved D-S decision-level fusion, as described below. The overall improved D-S decision-level fusion model is shown in Figure9. The steps in Figure 9 are outlined as follows:Step 1. The basic classification probability distribution of two classifiers is generated using classification resultsStep 2. Classifier weights are determined using classification the accuracy ratio (CAR) and classification correlation coefficient (CCC)Step 3. The adjusted classification probability distribution is generated using classifier weightsStep 4. The final classification results are calculated using D-S decision-level fusionFigure 9
Workflow graph of our improved D-S decision-level fusion model.


#### 2.4.1. Conversion from the Classification Result to Classification Probability Distribution

Based on (4), we calculate the products of membership degrees for the rVIS dimension of the VIS spectral feature vectors or the rNIR dimension of the NIR spectral vectors for one wood sample. Every product βl and its corresponding rule form one row of the matrix Tar:(11)Tar=Rule1dim1,…,Rule1dimr,β1Rule2dim1,…,Rule2dimr,β2⋮Rulendim1,…,Rulendimr,βn,where n is the maximum rule number such that n=951825 for rVIS=4 and n=1368640 for rNIR=4. Ruleldim1,…,Ruleldimr refers to rule l with product βl.Then, the rows withβl=0 are deleted in this matrix. The rule Ruleldim1,…,Ruleldimr in every row in the matrix Tar is checked to determine whether it belongs to the fuzzy rule set—Table 7—in Section 2.3.3. The rules in the fuzzy rule set remain, while those that are not in the set are deleted in order to form the matrix Tarpro:(12)Tarpro=Rulen1dim1,…,Rulen1dimr,βn1,Outn1Rulen2dim1,…,Rulen2dimr,βn2,Outn2⋮Rulenmdim1,…,Rulenmdimr,βnm,Outnm.The added final columnOutnl refers to the corresponding wood species. Some rules in Tarpro correspond to the same wood species (i.e., Outni=Outnj for i≠j). For an Outnl that corresponds to several rules, the maximum rule (i.e., with the largest βni) remains, while the others are deleted, so that the matrix Tarout is formed. Therefore, for one wood sample, the classification probability distribution can be computed as follows:(13)Pnl=βnlsumβ,sumβ=∑nl=1nlastβnl,nl=1,2,…,nlast.Here,nlast is the number of Tarout. Note that, for wood species that do not exist in Tarout, their corresponding classification probabilities are set as 0. For example, the classification probability distribution in the VIS and NIR bands for a wood sample is shown in Table 8.Table 8
The basic classification probability distribution of the visible/near-infrared (VIS/NIR) fuzzy reasoning classifier (FRC).
Class labelVIS FRC (%)NIR FRC (%)10.000.0020.000.0030.000.0040.000.0050.000.00627.222.7570.740.0080.000.0090.000.00100.000.00110.000.001221.4593.17130.000.00141.680.00150.000.00160.000.001714.370.00180.000.00190.290.00200.000.00210.000.00220.000.00230.000.072413.150.17250.000.00260.000.00270.000.00284.700.00290.000.62300.000.00310.000.00320.000.00330.000.00340.000.00350.000.00360.000.00370.002.12380.000.00390.000.00400.000.00413.650.00424.320.00430.000.00440.000.35450.000.00467.920.00470.000.00480.000.75490.510.00500.000.00


#### 2.4.2. Weight Determination of VIS and NIR Fuzzy Rule Classifier

In this section, we propose a novel classifier’s weight determination based on the difference between the fuzzy classification accuracy ratio (CAR) and the correlation coefficient for the VIS and NIR bands using an analytical hierarchy process. In Section2.3.1, we concluded that the fuzzy classification accuracy was 90.20% after the PCA algorithm processing for rVIS=4, while it was 93.25% for rNIR=4 in the training set.Regarding the calculation of the classification correlation coefficient (CCC), the training set is used to calculate the classification probability distribution for each wood sample using (13). Then, the following equation is used to calculate the CCC for the VIS and NIR classifiers:(14)CCC=Covx,yσx⋅σy.Here,Covx,y refers to the covariance between the corrected and actual classification probability distributions. For instance, as described in Table 8, the actual classification probability distribution for one wood sample for the NIR and VIS classifiers was 0,0,0,0,0,2.75,0,…,0,0 and 0,0,0,0,0,27.22,0.74,…,0.51,0, respectively, while the corrected one was 0,0,0,0,0,1,0,…,0. The σx,σy represent the standard deviations for the corrected and actual classification probability distribution vectors in the training set, respectively. The computed fuzzy CCC was 0.8073 after PCA algorithm processing for rVIS=4, whereas it was 0.8862 for rNIR=4.The difference in the CAR wasDiffCAR=CARVIS−CARNIR=0.0350, while that of CCC was DiffCCC=CCCVIS−CCCNIR=0.0789. The membership functions are shown in Figure 10. The corresponding credibility for these interval differences is shown in Table 9. We observed that the DiffCAR was in the 1st interval, which indicated that the VIS fuzzy and NIR fuzzy classifiers had the same credibility in view of the CAR, while DiffCCC was in the 2nd interval, which indicated that the NIR fuzzy classifier was more credible than the VIS classifier in view of the CCC. To determine the classifier’s weight using (17), we first need to compute the classifier’s scores using (15) and then compute the mean score using (16):(15)ScoreVIS=ScoreVISCCC×ScoreVISCAR=1×1=1,ScoreNIR=ScoreNIRCCC×ScoreNIRCAR=1×2=2,(16)Scoremean=ScoreVIS+ScoreNIR2,(17)WeightVIS=ScoreVISScoremean=23,WeightNIR=ScoreNIRScoremean=43.Figure 10
Membership degree functions for CAR and CCC differences.Table 9
The relationship between the classification accuracy ratio (CAR) or classification correlation coefficient (CCC) difference interval and its credibility.
RR and CC differenceCredibilityDescription1st interval1The same trusted2nd interval2Between 1 and 33rd interval3A little trusted4th interval4Between 3 and 55th interval5Obviously trusted6th interval6Between 5 and 77th interval7Strongly trusted8th interval8Between 7 and 99th interval9Extremely trusted


#### 2.4.3. Improved D-S Decision-Level Fusion Based on the Classifier’s Weight

In this section, we modified the classification probability distribution, as shown in Table8, in the VIS and NIR bands using the weight of the classifier. First, the maximum probability was modified using (18), and then, we computed the sum of this modified maximum probability with the other 19 probabilities using (19). Finally, we obtained the modified classification probability distribution using (20). As an example, the classification probability distribution in Table 8 was modified in this manner, as shown in Table 10.(18)Pmaxw=Weight×maxP1,P2,…,P20,(19)Psum=∑i=120Pi−maxP1,P2,…,P20+Pmaxw,(20)Pimod=PmaxwPsum,Pi=maxP1,P2,…,P20,PiPsum,Pi≠maxP1,P2,…,P20.Table 10
The adjustment classification probability distribution of the visible/near-infrared (VIS/NIR) fuzzy reasoning classifier (FRC).
Class labelVIS FRC (%)NIR FRC (%)10.000.0020.000.0030.000.0040.000.0050.000.00619.952.1070.810.0080.000.0090.000.00100.000.00110.000.001223.5994.78130.000.00141.850.00150.000.00160.000.001715.810.00180.000.00190.320.00200.000.00210.000.00220.000.00230.000.052414.460.13250.000.00260.000.00270.000.00285.170.00290.000.47300.000.00310.000.00320.000.00330.000.00340.000.00350.000.00360.000.00370.001.62380.000.00390.000.00400.000.00414.010.00424.750.00430.000.00440.000.28450.000.00468.710.00470.000.00480.000.57490.570.00500.000.00Finally, we used the modified VIS and NIR classification probability distributions to compute the normalized constant and composed mass function as follows (i.e.,mAi=Pimod):(21)K=∑i=150mVISAi⋅mNIRAi,massAi=1KmVISAi⋅mNIRAi.Here,Ai is the ith wood species with i=1,2,…,50. Based on these equations, we can compute 50 mass functions massAi,i=1,2,…,50. The first two largest massAi are defined as massmax1Ai,massmax2Ai, respectively. massf refers to the mass function for an uncertain set, and in our wood species, the recognition work massf=0. Wood sample x is then classified as wood species Aj with the following rules: massAj=massmax1Ai,ε1=0.15,ε2=0.01). Otherwise, the judgment is the “rejected classification”:(22)x∈Aj,ifmassmax1Ai−massmax2Ai>ε1,massf<ε2.


## 2.1. Wood Samples and Spectral Data Acquisition

Our wood dataset consists of 50 wood species, as shown in Table1 and Figure 1. These 50 wood species consist of softwood and hardwood species, which are representative tree species in the wood market. Moreover, this dataset also consists of some similar wood species (i.e., visually similar wood species and intragenus different species). Each wood sample was processed into a 2 × 2 × 3 cm block. We used the Ocean Optics USB2000-VIS-NIR microfiber spectrometer and an Ocean Optics FLAME-NIR microfiber spectrometer, visible and near-infrared (VIS/NIR) spectra of the wood samples being obtained using these devices. Fifty mean spectral curves were detected by using the spectrometer for each wood species—that is, there are 2500 VIS spectral curves and 2500 NIR spectral curves for 50 wood species. Our experimental setup consisted of a halogen lamp, a universal serial bus, a computer, a customized holder, a fiber spectrometer, and a section of optical fiber, as shown in Figure 2. Spectral acquisition was performed in a controlled environment at a temperature interval of 20±2°C. The VIS spectral band covered a range of 376.64–779.84 nm, with a spectral resolution of approximately 0.3 nm. The NIR spectral band covered a range of 950–1650 nm, with a spectral resolution of approximately 5.4 nm. The spectrometer parameter settings, spectral data acquisition, and data storage were conducted using the Spectrasuite software. The integration time was 300 ms, and the mean number of measurements at each point was 900. Before spectral acquisition, the reference and dark spectra were measured and stored, the reference spectra were acquired using a standard white panel of known 100% reflectance, and the dark spectra were acquired by blocking the radians. For each wood sample, four diffuse reflectance spectra were measured randomly using (1)—where IR,IB,andIW represented the received intensity, dark intensity, and white panel intensity, respectively—at different locations across the wood sample’s cross section. In fact, wood cross section has plentiful wood structures such as pores and parenchyma, making its spectra more suitable for species recognition, which is superior to radial direction and tangential direction in wood species recognition [26] and wood density prediction [13]. Subsequently, the mean spectrum of each wood sample was calculated and stored for subsequent spectral analysis and species classification. Figures 3 and 4 show the acquired mean spectra of the 50 wood species with standard normal variables (SNVs).(1)ref=IR−IBIW−IB.Table 1
The names of the wood species.
Class labelLatin name1Pterocarpus soyauxii2Ulmus glabra3Calophyllum brasiliense4Intsia bijuga5Tectona grandis6Pouteria speciosa7Quercus mongolica8Magnolia fordiana9Guibourtia ehie10Terninalia catappa11Cinnamomum camphora12Guibourtia demeusei13Swintonia florbunda14Fraxinus mandshurica15Pometia pinnata16Dipterocarpus alatus17Vernicia fordii18Sophora japonica19Robinia pseudoacacia20Quercus acutissima21Populus alba22Fraxinus chinensis23Pinus sylvestris24Populus tomentosa25Betula alnoides26Betula platyphylla27Platanus orientalis28Picea asperata29Larix gmelinii30Salix matsudana31Amygdalus davidiana32Juglans mandshurica33Pinus koraiensis34Populus cathayana35Tona ciliate36Prunus avium37Pinus massoniana38Aucoumea klaineana39Shorea contorta40Entandrophragma candollei41Millettia laurentii42Swietenia mahagoni43Rhodamnia dumetorum44Cyclobalanopsis glauca45Shorea laevis46Chamaecyparis nootkatensis47Juglans nigra48Tilia mandshurica49Pseudotsuga menziesii50Pinups radiataFigure 1
Wood samples for 50 wood species, and the order is the same as that in Table1 (see Table 1 for specific wood species names).Figure 2
Our spectral acquisition system.Figure 3
VIS spectral reflectance curves for 50 wood species with SNV.Figure 4
NIR spectral reflectance curves for 50 wood species with SNV.The spectral range of the USB2000-VIS-NIR spectrometer was 340–1027 nm. Both ends of this spectral range can be noisy, so the useful spectral range is 376.64–779.84 nm. The spectral data in the VIS band may be variable as the color of a wood sample may change with changing environmental conditions. To avoid this, we maintained a stable environment during spectral acquisition and wood sample preservation. The NIR band of 950–1650 nm is relatively stable and can be used to characterize different wood properties to some extent. Therefore, these two bands were processed using different fuzzy classifiers—that is, with different membership functions and fuzzy rules—the two classification results of which were further processed using an improved decision-level fusion based on the D-S evidential theory.


## 2.2. Spectral Dimension Reduction

For each spectral curve, the VIS/NIR band includes thousands of spectral data, so that the spectral dimension is very large. Consequently, each spectral curve contains redundant information, which reduces the wood species classification accuracy and speed. We used principal component analysis (PCA) and the T-distributed stochastic neighbor embedding (T-SNE) algorithms to compare and reduce the spectral dimension results. The PCA algorithm is a transformation algorithm in multivariate statistics, which is based on the variance maximization of a mapped low-dimension vector. The procedure is as follows: First, the initial dataset matrix is defined asAm×n=a1,…,an—where m and n are the dimension and number of feature vectors, respectively. The mean vector is computed as u=1/n∑i=1nai. Second, we compute xi=ai−u to form Xm×n=x1,…,xn. Third, the k largest eigenvalues of XXT are selected, their k corresponding eigenvectors ε1,…,εk forming a matrix D=ε1,…,εk. Finally, the new dataset matrix after dimension reduction is computed as DT×X=Pk×nk<m.Additionally, the T-SNE algorithm was also used for spectral dimension reduction. This algorithm performs nonlinear dimension reduction, an improvement on the original SNE algorithm [27]. The algorithm is based on the invariant data distribution probability of the mapped low-dimensional vector. Here, the symbol “T” in T-SNE represents the t-distribution, the freedom of the t-distribution being 1 in this study. The graphs of the three-dimensional (3D) spectral vectors for the VIS and NIR bands after spectral dimension reduction using the PCA and T-SNE algorithms are shown in Figure 5. The contribution rate (CR) and cumulative contribution rate (CCR) of the first ten principal components are shown in Figure 6 and Table 2 for the VIS and NIR bands. In Figure 5, the wood sample’s 3D spectral vectors were acquired using the PCA and T-SNE algorithms and are shown with 50 different colors for the 50 wood species. The best case is shown in Figure 5(b), where the wood samples were the most dispersed.Figure 5
Spectral dimension reduction 3D results: (a) PCA for the VIS band; (b) PCA for the NIR band; (c) T-SNE for the VIS band; and (d) T-SNE for the NIR band.
(a)(b)(c)(d)Figure 6
Contribution of PC by using PCA: (a) contribution rate of PC for the VIS band; (b) cumulative contribution rate of PC for the VIS band; (c) contribution rate of PC for the NIR band; and (d) cumulative contribution rate of PC for the NIR band.
(a)(b)(c)(d)Table 2
The contribution rate (CR) and cumulative contribution rate (CCR) of the principal components (PCs) for visible (VIS) and near-infrared (NIR) spectral data.
PC01PC02PC03PC04PC05PC06PC07PC08PC09PC10VIS CR0.88040.07260.03010.00700.00610.00180.000749820.000559080.000478820.00027888VIS CCR0.88040.95290.98300.99000.99610.99790.99860.99920.99970.9999NIR CR0.82150.14680.01550.00970.00290.00210.000823300.000230930.000173110.00010637NIR CCR0.82150.96830.98380.99350.99650.99870.99940.99970.99980.9999


## 2.3. Fuzzy Rule Classifier

A fuzzy rule classifier is a fuzzy reasoning system based on fuzzy linguistic rules, its core component being a fuzzy rule set. When an input sample is transformed into the rule set of one wood species, this sample is then classified as a wood species. The overall fuzzy reasoning system is shown in Figure7 and consists of two parts: the training and testing processes. The steps in Figure 7 are presented as follows.Step 1. The membership functions are set to fuzzify the training sample’s feature and generate the training sample’s fuzzy rulesStep 2. Fuzzy rules are adjusted by using a corrected confidence coefficientStep 3. The fuzzy rule set is generatedStep 4. The testing sample’s feature is fuzzified, and the generated rule is compared with the fuzzy rule set for wood species classificationFigure 7
Workflow graph of our fuzzy rule classification system.The training process consisted of three steps. First, membership functions were used to fulfill the fuzzification of the training dataset. Here, the membership functions could be a triangular function, trapezoid function, or Gaussian function. Second, fuzzy rules were generated based on the wood species of the wood samples in the training dataset. A fuzzy rule was defined as “IF … AND …, THEN …” using the conjunction or disjunction operation. Third, the fuzzy rules required modification using a confidence coefficient to form a perfect fuzzy rule set.In the testing process, the testing dataset was added to the trained fuzzy rule classifier, and the same membership functions were used to fulfill its fuzzification. In this way, a corresponding fuzzy rule of a testing sample could be obtained, and this rule was compared with the generated perfect fuzzy rule set to obtain the classified wood species. This species was then compared with the correctly labeled species of the testing sample to evaluate the performance of the fuzzy rule classifier. If the corresponding fuzzy rule of a testing sample was not found in the perfect fuzzy rule set, the sample was classified as an unknown species.


### 2.3.1. Fuzzification of the Feature Vector

Here, the feature vector refers to the spectral vector after dimension reduction. This fuzzification step transforms spectral feature vectors into linguistic variables. A linguistic variable is defined using a triple valueV,X,TV, where V is a variable (e.g., PC1) defined on a set of reference X, X is the universe of discourse (field of variation of V), and TV is the vocabulary chosen to describe the values of V in a symbolic way. The set TV=A1,A2,… contains the normalized fuzzy subsets of X, and each fuzzy subset Ai is defined by the membership degree uAi.For example, the wood spectral feature vector is obtained using the PCA algorithm. The fourth principal component (PC4) of the first ten wood species is shown in Table3 for the NIR band, where the maximum, minimum, mean, and median values of PC4 are shown. Thus, we can design the membership functions to divide the NIR PC4 (i.e., the 4th dimension) into twenty-six intervals TV=A1,A2,…,A26 based on these values, as shown in Figure 8.Table 3
Principal component 4 (PC4) data for the first ten wood species in the near-infrared (NIR) band.
Wood speciesMinimum valueMean valueMedian valueMaximum valuePterocarpus soyauxii−0.292834701−0.16041152−0.1699747120.007724295Ulmus glabra0.0253157880.1957505660.2108186090.363952969Calophyllum brasiliense−0.192778352−0.117200877−0.117229875−0.034786326Intsia bijuga−0.389917083−0.139350711−0.1377726120.114471138Tectona grandis−0.0575578260.1481586360.1533149030.280022623Pouteria speciosa−0.0950309850.0538110880.0500285470.191835329Quercus mongolica−0.0629643380.0561465120.0465165520.338022639Magnolia fordiana−0.154656742−0.037434328−0.0481849820.126992175Guibourtia ehie−0.338868726−0.178740936−0.2012918660.085960311Terninalia catappa−0.1871783530.0607163560.0537035390.267102296Figure 8
PC4 is divided into 26 intervals by use of membership functions for the NIR band.As the different spectral PCs or dimensions may be divided into different intervals, the overall number of fuzzy rules is the product of the interval number of different PCs or dimensions:(2)Nrules=∏V=1NCardTV,where N is the dimension of the spectral feature vectors and CardTV is the number of intervals for variable V (i.e., the element of the spectral feature vector). In fact, Nrules can be determined by both N and CardTV. Therefore, a large N or CardTV produces a large Nrules resulting in high computational complexity. In other words, N and CardTV should be designed to be as small as possible in view of the recognition accuracy of our fuzzy rule classifier. If they cannot be simultaneously small, the dimension N should be as small as possible.For instance, if the PCA algorithm is used for wood spectral dimension reduction, the CCR should be above 99% in view of the PC number. As can be seen from Table2, the CCR of the first four PCs reaches 99% and 99.35% for the VIS and NIR bands, respectively, but remains approximately stable when N>4, so we should set N≥4.After several tests with the PCA algorithm,N and CardTV were as follows: for the VIS band, CardT1=37,CardT2=35,CardT3=25, CardT4=21,CardT5=15,and CardT6=2. For the NIR band, CardT1=47,CardT2=40,CardT3=28, CardT4=26,CardT5=20,and CardT6=2. The triangular, trapezoid, and triangular-trapezoid functions were used and compared 50 times—in terms of the ORA and mean training time requirement (i.e., the wood sample number of the training set was 2000) for the fuzzy rule set—as described in Tables 4 and 5 for the VIS and NIR bands, respectively. The maximum and practical Nrules in terms of N and CardTV are listed in Table 6. We observed that the training time requirement for the fuzzy rule set was practically invariant with regard to the fuzzy classifiers based on different membership functions. However, this time requirement was only relevant to the N dimension of the spectral feature vectors. In fact, both the time requirement and the Nrules increased rapidly when the dimension N increased. Moreover, the overall recognition accuracy in terms of the triangular-function-based fuzzy classifier increased when the dimension N increased, but the trapezoid-function- or triangular-trapezoid-function-based classifier remained practically invariant when the dimensions were N≥4 and N≥6 for the VIS and NIR bands, respectively. Finally, using our fuzzy classifier, the optimal trapezoid function parameters were dimension N=37, CardT1=35,CardT2=25,CardT3=25, and CardT4=21 for the VIS band and N=4,CardT1=47,CardT2=40,CardT3=28,and CardT4=26 for the NIR band.Table 4
Overall recognition accuracy (ORA) and training time requirement (TR) of differentN and membership functions in the visible (VIS) band.
DimensionNTriangular functionTrapezoid functionTriangular-trapezoidORA (%)TR (s)ORA (%)TR (s)ORA (%)TR (s)375.651051.2776.851154.1277.801219.26489.0524393.2489.6025128.7590.2024983.20589.60312764.5290.05299023.2090.25327279.92690.20556719.4790.40469466.5390.65483718.36Table 5
Overall recognition accuracy (ORA) and training time requirement (TR) of differentN and membership functions in the near-infrared (NIR) band.
DimensionNTriangular functionTrapezoid functionTriangular-trapezoidORA (%)TR (s)ORA (%)TR (s)ORA (%)TR (s)377.651822.2382.801733.4681.151807.12490.2545125.0292.9044783.2493.2548353.50591.55657271.1593.10631285.4692.85718375.61692.051038488.1893.05940615.3493.351223481.25Table 6
Maximum and practical fuzzy rule numbers.
DimensionN345(VIS) maximum fuzzy rule number4532595182514277375(VIS) practical fuzzy rule number98713621475(NIR) maximum fuzzy rule number52640136864027372800(NIR) practical fuzzy rule number113516741689


### 2.3.2. Fuzzy Rule Generation

After the fuzzification of the spectral feature vectors, the fuzzy rules in the form of “IF … AND …, THEN …” required definition. For example, if three linguistic variables are considered for inputV1,V2,V3 and the output is wood species Y, the fuzzy rule is as follows:(3)IFV1isAIANDV2isBJANDV3isCKTHENYisClassl.This expression indicates that whenV1 is classified as AI, V2 is classified as BJ …, and the output class is Classl. Therefore, we need to calculate the membership degrees uAi,uBj,uCk for input V1,V2,V3. In this expression, “AND” is a Cartesian product between the linguistic variables and the operation is performed with a T-Norm, as follows:(4)Tx,y,z=x×y×z.This equation is then used to calculate the product of the membership degrees for the spectral linguistic variablesV1,V2,V3:(5)βClassls=uAi×uBj×uCk.For one wood sample of wood class/speciesl, there are often some products of the membership degrees βClassls≠0,s=1,2,…,S. For example, if uA1,uA3,uA4,uB1,uB5,uC1 are not equal to 0, we obtain 3×2×1=6 products of the membership degrees for one wood sample (i.e., βClassls,s=1,2,…,6). We should then choose the largest product to form the corresponding rule. Thus, we obtain a fuzzy rule for wood class/species l as follows:(6)maxβClassls=uAI×uBJ×uCK.


### 2.3.3. Fuzzy Rule Adjustment

When the fuzzy rule is generated, there are usually several rules with the same judgment condition (i.e., the same “IF … AND …,”) but different classification results (i.e., different “THEN …”). Consequently, fuzzy rule adjustment is usually required to add a confidence coefficient (CC) to each fuzzy rule.First, for one wood sample of wood class/speciesl, the sum of the products of the membership degrees βClassls≠0,s=1,2,…,S is calculated as follows:(7)βsum=∑s=1SβClassls.Then, the mean value is calculated using(8)βmean=βsum−maxβClasslsS−1.Thus, we can compute the CC of the fuzzy rule produced as follows:(9)CC=maxβClassls−βmeanβsum.Moreover, when the same rules are produced by other samples, the CC of the fuzzy rule should be increased as follows:(10)CC=CC+α1−CC.If the same rule is not produced by other samples, the CC of this fuzzy rule remains invariant. Some final rules with their CCs are listed in Table7. In practical classification work, when there are rules that have the same judgment condition but different classification results, the final classification is determined by the fuzzy rule with the largest CC.Table 7
The fuzzy rule set with a confidence coefficient (CC) for the visible (VIS) band.
ABCDCCWood species224860.9939Pinups radiata5209150.9876Tilia mandshurica282920150.9072Juglans nigra………………1721260.7993Entandrophragma candollei3231160.6161Chamaecyparis nootkatensis………………


## 2.3.1. Fuzzification of the Feature Vector

Here, the feature vector refers to the spectral vector after dimension reduction. This fuzzification step transforms spectral feature vectors into linguistic variables. A linguistic variable is defined using a triple valueV,X,TV, where V is a variable (e.g., PC1) defined on a set of reference X, X is the universe of discourse (field of variation of V), and TV is the vocabulary chosen to describe the values of V in a symbolic way. The set TV=A1,A2,… contains the normalized fuzzy subsets of X, and each fuzzy subset Ai is defined by the membership degree uAi.For example, the wood spectral feature vector is obtained using the PCA algorithm. The fourth principal component (PC4) of the first ten wood species is shown in Table3 for the NIR band, where the maximum, minimum, mean, and median values of PC4 are shown. Thus, we can design the membership functions to divide the NIR PC4 (i.e., the 4th dimension) into twenty-six intervals TV=A1,A2,…,A26 based on these values, as shown in Figure 8.Table 3
Principal component 4 (PC4) data for the first ten wood species in the near-infrared (NIR) band.
Wood speciesMinimum valueMean valueMedian valueMaximum valuePterocarpus soyauxii−0.292834701−0.16041152−0.1699747120.007724295Ulmus glabra0.0253157880.1957505660.2108186090.363952969Calophyllum brasiliense−0.192778352−0.117200877−0.117229875−0.034786326Intsia bijuga−0.389917083−0.139350711−0.1377726120.114471138Tectona grandis−0.0575578260.1481586360.1533149030.280022623Pouteria speciosa−0.0950309850.0538110880.0500285470.191835329Quercus mongolica−0.0629643380.0561465120.0465165520.338022639Magnolia fordiana−0.154656742−0.037434328−0.0481849820.126992175Guibourtia ehie−0.338868726−0.178740936−0.2012918660.085960311Terninalia catappa−0.1871783530.0607163560.0537035390.267102296Figure 8
PC4 is divided into 26 intervals by use of membership functions for the NIR band.As the different spectral PCs or dimensions may be divided into different intervals, the overall number of fuzzy rules is the product of the interval number of different PCs or dimensions:(2)Nrules=∏V=1NCardTV,where N is the dimension of the spectral feature vectors and CardTV is the number of intervals for variable V (i.e., the element of the spectral feature vector). In fact, Nrules can be determined by both N and CardTV. Therefore, a large N or CardTV produces a large Nrules resulting in high computational complexity. In other words, N and CardTV should be designed to be as small as possible in view of the recognition accuracy of our fuzzy rule classifier. If they cannot be simultaneously small, the dimension N should be as small as possible.For instance, if the PCA algorithm is used for wood spectral dimension reduction, the CCR should be above 99% in view of the PC number. As can be seen from Table2, the CCR of the first four PCs reaches 99% and 99.35% for the VIS and NIR bands, respectively, but remains approximately stable when N>4, so we should set N≥4.After several tests with the PCA algorithm,N and CardTV were as follows: for the VIS band, CardT1=37,CardT2=35,CardT3=25, CardT4=21,CardT5=15,and CardT6=2. For the NIR band, CardT1=47,CardT2=40,CardT3=28, CardT4=26,CardT5=20,and CardT6=2. The triangular, trapezoid, and triangular-trapezoid functions were used and compared 50 times—in terms of the ORA and mean training time requirement (i.e., the wood sample number of the training set was 2000) for the fuzzy rule set—as described in Tables 4 and 5 for the VIS and NIR bands, respectively. The maximum and practical Nrules in terms of N and CardTV are listed in Table 6. We observed that the training time requirement for the fuzzy rule set was practically invariant with regard to the fuzzy classifiers based on different membership functions. However, this time requirement was only relevant to the N dimension of the spectral feature vectors. In fact, both the time requirement and the Nrules increased rapidly when the dimension N increased. Moreover, the overall recognition accuracy in terms of the triangular-function-based fuzzy classifier increased when the dimension N increased, but the trapezoid-function- or triangular-trapezoid-function-based classifier remained practically invariant when the dimensions were N≥4 and N≥6 for the VIS and NIR bands, respectively. Finally, using our fuzzy classifier, the optimal trapezoid function parameters were dimension N=37, CardT1=35,CardT2=25,CardT3=25, and CardT4=21 for the VIS band and N=4,CardT1=47,CardT2=40,CardT3=28,and CardT4=26 for the NIR band.Table 4
Overall recognition accuracy (ORA) and training time requirement (TR) of differentN and membership functions in the visible (VIS) band.
DimensionNTriangular functionTrapezoid functionTriangular-trapezoidORA (%)TR (s)ORA (%)TR (s)ORA (%)TR (s)375.651051.2776.851154.1277.801219.26489.0524393.2489.6025128.7590.2024983.20589.60312764.5290.05299023.2090.25327279.92690.20556719.4790.40469466.5390.65483718.36Table 5
Overall recognition accuracy (ORA) and training time requirement (TR) of differentN and membership functions in the near-infrared (NIR) band.
DimensionNTriangular functionTrapezoid functionTriangular-trapezoidORA (%)TR (s)ORA (%)TR (s)ORA (%)TR (s)377.651822.2382.801733.4681.151807.12490.2545125.0292.9044783.2493.2548353.50591.55657271.1593.10631285.4692.85718375.61692.051038488.1893.05940615.3493.351223481.25Table 6
Maximum and practical fuzzy rule numbers.
DimensionN345(VIS) maximum fuzzy rule number4532595182514277375(VIS) practical fuzzy rule number98713621475(NIR) maximum fuzzy rule number52640136864027372800(NIR) practical fuzzy rule number113516741689


## 2.3.2. Fuzzy Rule Generation

After the fuzzification of the spectral feature vectors, the fuzzy rules in the form of “IF … AND …, THEN …” required definition. For example, if three linguistic variables are considered for inputV1,V2,V3 and the output is wood species Y, the fuzzy rule is as follows:(3)IFV1isAIANDV2isBJANDV3isCKTHENYisClassl.This expression indicates that whenV1 is classified as AI, V2 is classified as BJ …, and the output class is Classl. Therefore, we need to calculate the membership degrees uAi,uBj,uCk for input V1,V2,V3. In this expression, “AND” is a Cartesian product between the linguistic variables and the operation is performed with a T-Norm, as follows:(4)Tx,y,z=x×y×z.This equation is then used to calculate the product of the membership degrees for the spectral linguistic variablesV1,V2,V3:(5)βClassls=uAi×uBj×uCk.For one wood sample of wood class/speciesl, there are often some products of the membership degrees βClassls≠0,s=1,2,…,S. For example, if uA1,uA3,uA4,uB1,uB5,uC1 are not equal to 0, we obtain 3×2×1=6 products of the membership degrees for one wood sample (i.e., βClassls,s=1,2,…,6). We should then choose the largest product to form the corresponding rule. Thus, we obtain a fuzzy rule for wood class/species l as follows:(6)maxβClassls=uAI×uBJ×uCK.


## 2.3.3. Fuzzy Rule Adjustment

When the fuzzy rule is generated, there are usually several rules with the same judgment condition (i.e., the same “IF … AND …,”) but different classification results (i.e., different “THEN …”). Consequently, fuzzy rule adjustment is usually required to add a confidence coefficient (CC) to each fuzzy rule.First, for one wood sample of wood class/speciesl, the sum of the products of the membership degrees βClassls≠0,s=1,2,…,S is calculated as follows:(7)βsum=∑s=1SβClassls.Then, the mean value is calculated using(8)βmean=βsum−maxβClasslsS−1.Thus, we can compute the CC of the fuzzy rule produced as follows:(9)CC=maxβClassls−βmeanβsum.Moreover, when the same rules are produced by other samples, the CC of the fuzzy rule should be increased as follows:(10)CC=CC+α1−CC.If the same rule is not produced by other samples, the CC of this fuzzy rule remains invariant. Some final rules with their CCs are listed in Table7. In practical classification work, when there are rules that have the same judgment condition but different classification results, the final classification is determined by the fuzzy rule with the largest CC.Table 7
The fuzzy rule set with a confidence coefficient (CC) for the visible (VIS) band.
ABCDCCWood species224860.9939Pinups radiata5209150.9876Tilia mandshurica282920150.9072Juglans nigra………………1721260.7993Entandrophragma candollei3231160.6161Chamaecyparis nootkatensis………………


## 2.4. Decision-Level Fusion

The D-S evidential theory [28] is an effective decision-level fusion scheme, but the classifier’s reliability is not considered fully when each classifier’s result is converted into a classification probability distribution before the decision-level fusion. To solve this problem, we proposed an improved D-S decision-level fusion method that determines each classifier’s weight in view of the differences in the classification accuracy ratio and correlation coefficient.As the NIR band is more stable than the VIS band, these two bands should be processed using different fuzzy parameters (e.g., different membership functions). Consequently, spectral dimension reduction and fuzzy rule classification were applied to the two bands, respectively, so that the two classification results could be fused with our improved D-S decision-level fusion, as described below. The overall improved D-S decision-level fusion model is shown in Figure9. The steps in Figure 9 are outlined as follows:Step 1. The basic classification probability distribution of two classifiers is generated using classification resultsStep 2. Classifier weights are determined using classification the accuracy ratio (CAR) and classification correlation coefficient (CCC)Step 3. The adjusted classification probability distribution is generated using classifier weightsStep 4. The final classification results are calculated using D-S decision-level fusionFigure 9
Workflow graph of our improved D-S decision-level fusion model.


### 2.4.1. Conversion from the Classification Result to Classification Probability Distribution

Based on (4), we calculate the products of membership degrees for the rVIS dimension of the VIS spectral feature vectors or the rNIR dimension of the NIR spectral vectors for one wood sample. Every product βl and its corresponding rule form one row of the matrix Tar:(11)Tar=Rule1dim1,…,Rule1dimr,β1Rule2dim1,…,Rule2dimr,β2⋮Rulendim1,…,Rulendimr,βn,where n is the maximum rule number such that n=951825 for rVIS=4 and n=1368640 for rNIR=4. Ruleldim1,…,Ruleldimr refers to rule l with product βl.Then, the rows withβl=0 are deleted in this matrix. The rule Ruleldim1,…,Ruleldimr in every row in the matrix Tar is checked to determine whether it belongs to the fuzzy rule set—Table 7—in Section 2.3.3. The rules in the fuzzy rule set remain, while those that are not in the set are deleted in order to form the matrix Tarpro:(12)Tarpro=Rulen1dim1,…,Rulen1dimr,βn1,Outn1Rulen2dim1,…,Rulen2dimr,βn2,Outn2⋮Rulenmdim1,…,Rulenmdimr,βnm,Outnm.The added final columnOutnl refers to the corresponding wood species. Some rules in Tarpro correspond to the same wood species (i.e., Outni=Outnj for i≠j). For an Outnl that corresponds to several rules, the maximum rule (i.e., with the largest βni) remains, while the others are deleted, so that the matrix Tarout is formed. Therefore, for one wood sample, the classification probability distribution can be computed as follows:(13)Pnl=βnlsumβ,sumβ=∑nl=1nlastβnl,nl=1,2,…,nlast.Here,nlast is the number of Tarout. Note that, for wood species that do not exist in Tarout, their corresponding classification probabilities are set as 0. For example, the classification probability distribution in the VIS and NIR bands for a wood sample is shown in Table 8.Table 8
The basic classification probability distribution of the visible/near-infrared (VIS/NIR) fuzzy reasoning classifier (FRC).
Class labelVIS FRC (%)NIR FRC (%)10.000.0020.000.0030.000.0040.000.0050.000.00627.222.7570.740.0080.000.0090.000.00100.000.00110.000.001221.4593.17130.000.00141.680.00150.000.00160.000.001714.370.00180.000.00190.290.00200.000.00210.000.00220.000.00230.000.072413.150.17250.000.00260.000.00270.000.00284.700.00290.000.62300.000.00310.000.00320.000.00330.000.00340.000.00350.000.00360.000.00370.002.12380.000.00390.000.00400.000.00413.650.00424.320.00430.000.00440.000.35450.000.00467.920.00470.000.00480.000.75490.510.00500.000.00


### 2.4.2. Weight Determination of VIS and NIR Fuzzy Rule Classifier

In this section, we propose a novel classifier’s weight determination based on the difference between the fuzzy classification accuracy ratio (CAR) and the correlation coefficient for the VIS and NIR bands using an analytical hierarchy process. In Section2.3.1, we concluded that the fuzzy classification accuracy was 90.20% after the PCA algorithm processing for rVIS=4, while it was 93.25% for rNIR=4 in the training set.Regarding the calculation of the classification correlation coefficient (CCC), the training set is used to calculate the classification probability distribution for each wood sample using (13). Then, the following equation is used to calculate the CCC for the VIS and NIR classifiers:(14)CCC=Covx,yσx⋅σy.Here,Covx,y refers to the covariance between the corrected and actual classification probability distributions. For instance, as described in Table 8, the actual classification probability distribution for one wood sample for the NIR and VIS classifiers was 0,0,0,0,0,2.75,0,…,0,0 and 0,0,0,0,0,27.22,0.74,…,0.51,0, respectively, while the corrected one was 0,0,0,0,0,1,0,…,0. The σx,σy represent the standard deviations for the corrected and actual classification probability distribution vectors in the training set, respectively. The computed fuzzy CCC was 0.8073 after PCA algorithm processing for rVIS=4, whereas it was 0.8862 for rNIR=4.The difference in the CAR wasDiffCAR=CARVIS−CARNIR=0.0350, while that of CCC was DiffCCC=CCCVIS−CCCNIR=0.0789. The membership functions are shown in Figure 10. The corresponding credibility for these interval differences is shown in Table 9. We observed that the DiffCAR was in the 1st interval, which indicated that the VIS fuzzy and NIR fuzzy classifiers had the same credibility in view of the CAR, while DiffCCC was in the 2nd interval, which indicated that the NIR fuzzy classifier was more credible than the VIS classifier in view of the CCC. To determine the classifier’s weight using (17), we first need to compute the classifier’s scores using (15) and then compute the mean score using (16):(15)ScoreVIS=ScoreVISCCC×ScoreVISCAR=1×1=1,ScoreNIR=ScoreNIRCCC×ScoreNIRCAR=1×2=2,(16)Scoremean=ScoreVIS+ScoreNIR2,(17)WeightVIS=ScoreVISScoremean=23,WeightNIR=ScoreNIRScoremean=43.Figure 10
Membership degree functions for CAR and CCC differences.Table 9
The relationship between the classification accuracy ratio (CAR) or classification correlation coefficient (CCC) difference interval and its credibility.
RR and CC differenceCredibilityDescription1st interval1The same trusted2nd interval2Between 1 and 33rd interval3A little trusted4th interval4Between 3 and 55th interval5Obviously trusted6th interval6Between 5 and 77th interval7Strongly trusted8th interval8Between 7 and 99th interval9Extremely trusted


### 2.4.3. Improved D-S Decision-Level Fusion Based on the Classifier’s Weight

In this section, we modified the classification probability distribution, as shown in Table8, in the VIS and NIR bands using the weight of the classifier. First, the maximum probability was modified using (18), and then, we computed the sum of this modified maximum probability with the other 19 probabilities using (19). Finally, we obtained the modified classification probability distribution using (20). As an example, the classification probability distribution in Table 8 was modified in this manner, as shown in Table 10.(18)Pmaxw=Weight×maxP1,P2,…,P20,(19)Psum=∑i=120Pi−maxP1,P2,…,P20+Pmaxw,(20)Pimod=PmaxwPsum,Pi=maxP1,P2,…,P20,PiPsum,Pi≠maxP1,P2,…,P20.Table 10
The adjustment classification probability distribution of the visible/near-infrared (VIS/NIR) fuzzy reasoning classifier (FRC).
Class labelVIS FRC (%)NIR FRC (%)10.000.0020.000.0030.000.0040.000.0050.000.00619.952.1070.810.0080.000.0090.000.00100.000.00110.000.001223.5994.78130.000.00141.850.00150.000.00160.000.001715.810.00180.000.00190.320.00200.000.00210.000.00220.000.00230.000.052414.460.13250.000.00260.000.00270.000.00285.170.00290.000.47300.000.00310.000.00320.000.00330.000.00340.000.00350.000.00360.000.00370.001.62380.000.00390.000.00400.000.00414.010.00424.750.00430.000.00440.000.28450.000.00468.710.00470.000.00480.000.57490.570.00500.000.00Finally, we used the modified VIS and NIR classification probability distributions to compute the normalized constant and composed mass function as follows (i.e.,mAi=Pimod):(21)K=∑i=150mVISAi⋅mNIRAi,massAi=1KmVISAi⋅mNIRAi.Here,Ai is the ith wood species with i=1,2,…,50. Based on these equations, we can compute 50 mass functions massAi,i=1,2,…,50. The first two largest massAi are defined as massmax1Ai,massmax2Ai, respectively. massf refers to the mass function for an uncertain set, and in our wood species, the recognition work massf=0. Wood sample x is then classified as wood species Aj with the following rules: massAj=massmax1Ai,ε1=0.15,ε2=0.01). Otherwise, the judgment is the “rejected classification”:(22)x∈Aj,ifmassmax1Ai−massmax2Ai>ε1,massf<ε2.


## 2.4.1. Conversion from the Classification Result to Classification Probability Distribution

Based on (4), we calculate the products of membership degrees for the rVIS dimension of the VIS spectral feature vectors or the rNIR dimension of the NIR spectral vectors for one wood sample. Every product βl and its corresponding rule form one row of the matrix Tar:(11)Tar=Rule1dim1,…,Rule1dimr,β1Rule2dim1,…,Rule2dimr,β2⋮Rulendim1,…,Rulendimr,βn,where n is the maximum rule number such that n=951825 for rVIS=4 and n=1368640 for rNIR=4. Ruleldim1,…,Ruleldimr refers to rule l with product βl.Then, the rows withβl=0 are deleted in this matrix. The rule Ruleldim1,…,Ruleldimr in every row in the matrix Tar is checked to determine whether it belongs to the fuzzy rule set—Table 7—in Section 2.3.3. The rules in the fuzzy rule set remain, while those that are not in the set are deleted in order to form the matrix Tarpro:(12)Tarpro=Rulen1dim1,…,Rulen1dimr,βn1,Outn1Rulen2dim1,…,Rulen2dimr,βn2,Outn2⋮Rulenmdim1,…,Rulenmdimr,βnm,Outnm.The added final columnOutnl refers to the corresponding wood species. Some rules in Tarpro correspond to the same wood species (i.e., Outni=Outnj for i≠j). For an Outnl that corresponds to several rules, the maximum rule (i.e., with the largest βni) remains, while the others are deleted, so that the matrix Tarout is formed. Therefore, for one wood sample, the classification probability distribution can be computed as follows:(13)Pnl=βnlsumβ,sumβ=∑nl=1nlastβnl,nl=1,2,…,nlast.Here,nlast is the number of Tarout. Note that, for wood species that do not exist in Tarout, their corresponding classification probabilities are set as 0. For example, the classification probability distribution in the VIS and NIR bands for a wood sample is shown in Table 8.Table 8
The basic classification probability distribution of the visible/near-infrared (VIS/NIR) fuzzy reasoning classifier (FRC).
Class labelVIS FRC (%)NIR FRC (%)10.000.0020.000.0030.000.0040.000.0050.000.00627.222.7570.740.0080.000.0090.000.00100.000.00110.000.001221.4593.17130.000.00141.680.00150.000.00160.000.001714.370.00180.000.00190.290.00200.000.00210.000.00220.000.00230.000.072413.150.17250.000.00260.000.00270.000.00284.700.00290.000.62300.000.00310.000.00320.000.00330.000.00340.000.00350.000.00360.000.00370.002.12380.000.00390.000.00400.000.00413.650.00424.320.00430.000.00440.000.35450.000.00467.920.00470.000.00480.000.75490.510.00500.000.00


## 2.4.2. Weight Determination of VIS and NIR Fuzzy Rule Classifier

In this section, we propose a novel classifier’s weight determination based on the difference between the fuzzy classification accuracy ratio (CAR) and the correlation coefficient for the VIS and NIR bands using an analytical hierarchy process. In Section2.3.1, we concluded that the fuzzy classification accuracy was 90.20% after the PCA algorithm processing for rVIS=4, while it was 93.25% for rNIR=4 in the training set.Regarding the calculation of the classification correlation coefficient (CCC), the training set is used to calculate the classification probability distribution for each wood sample using (13). Then, the following equation is used to calculate the CCC for the VIS and NIR classifiers:(14)CCC=Covx,yσx⋅σy.Here,Covx,y refers to the covariance between the corrected and actual classification probability distributions. For instance, as described in Table 8, the actual classification probability distribution for one wood sample for the NIR and VIS classifiers was 0,0,0,0,0,2.75,0,…,0,0 and 0,0,0,0,0,27.22,0.74,…,0.51,0, respectively, while the corrected one was 0,0,0,0,0,1,0,…,0. The σx,σy represent the standard deviations for the corrected and actual classification probability distribution vectors in the training set, respectively. The computed fuzzy CCC was 0.8073 after PCA algorithm processing for rVIS=4, whereas it was 0.8862 for rNIR=4.The difference in the CAR wasDiffCAR=CARVIS−CARNIR=0.0350, while that of CCC was DiffCCC=CCCVIS−CCCNIR=0.0789. The membership functions are shown in Figure 10. The corresponding credibility for these interval differences is shown in Table 9. We observed that the DiffCAR was in the 1st interval, which indicated that the VIS fuzzy and NIR fuzzy classifiers had the same credibility in view of the CAR, while DiffCCC was in the 2nd interval, which indicated that the NIR fuzzy classifier was more credible than the VIS classifier in view of the CCC. To determine the classifier’s weight using (17), we first need to compute the classifier’s scores using (15) and then compute the mean score using (16):(15)ScoreVIS=ScoreVISCCC×ScoreVISCAR=1×1=1,ScoreNIR=ScoreNIRCCC×ScoreNIRCAR=1×2=2,(16)Scoremean=ScoreVIS+ScoreNIR2,(17)WeightVIS=ScoreVISScoremean=23,WeightNIR=ScoreNIRScoremean=43.Figure 10
Membership degree functions for CAR and CCC differences.Table 9
The relationship between the classification accuracy ratio (CAR) or classification correlation coefficient (CCC) difference interval and its credibility.
RR and CC differenceCredibilityDescription1st interval1The same trusted2nd interval2Between 1 and 33rd interval3A little trusted4th interval4Between 3 and 55th interval5Obviously trusted6th interval6Between 5 and 77th interval7Strongly trusted8th interval8Between 7 and 99th interval9Extremely trusted


## 2.4.3. Improved D-S Decision-Level Fusion Based on the Classifier’s Weight

In this section, we modified the classification probability distribution, as shown in Table8, in the VIS and NIR bands using the weight of the classifier. First, the maximum probability was modified using (18), and then, we computed the sum of this modified maximum probability with the other 19 probabilities using (19). Finally, we obtained the modified classification probability distribution using (20). As an example, the classification probability distribution in Table 8 was modified in this manner, as shown in Table 10.(18)Pmaxw=Weight×maxP1,P2,…,P20,(19)Psum=∑i=120Pi−maxP1,P2,…,P20+Pmaxw,(20)Pimod=PmaxwPsum,Pi=maxP1,P2,…,P20,PiPsum,Pi≠maxP1,P2,…,P20.Table 10
The adjustment classification probability distribution of the visible/near-infrared (VIS/NIR) fuzzy reasoning classifier (FRC).
Class labelVIS FRC (%)NIR FRC (%)10.000.0020.000.0030.000.0040.000.0050.000.00619.952.1070.810.0080.000.0090.000.00100.000.00110.000.001223.5994.78130.000.00141.850.00150.000.00160.000.001715.810.00180.000.00190.320.00200.000.00210.000.00220.000.00230.000.052414.460.13250.000.00260.000.00270.000.00285.170.00290.000.47300.000.00310.000.00320.000.00330.000.00340.000.00350.000.00360.000.00370.001.62380.000.00390.000.00400.000.00414.010.00424.750.00430.000.00440.000.28450.000.00468.710.00470.000.00480.000.57490.570.00500.000.00Finally, we used the modified VIS and NIR classification probability distributions to compute the normalized constant and composed mass function as follows (i.e.,mAi=Pimod):(21)K=∑i=150mVISAi⋅mNIRAi,massAi=1KmVISAi⋅mNIRAi.Here,Ai is the ith wood species with i=1,2,…,50. Based on these equations, we can compute 50 mass functions massAi,i=1,2,…,50. The first two largest massAi are defined as massmax1Ai,massmax2Ai, respectively. massf refers to the mass function for an uncertain set, and in our wood species, the recognition work massf=0. Wood sample x is then classified as wood species Aj with the following rules: massAj=massmax1Ai,ε1=0.15,ε2=0.01). Otherwise, the judgment is the “rejected classification”:(22)x∈Aj,ifmassmax1Ai−massmax2Ai>ε1,massf<ε2.


## 3. Results and Comparisons

In our experiments, there were 2,500 spectral curves for 50 wood species. These samples were divided into a training set and a testing set using k-fold cross validation [29] with k=5, so that the training set consisted of 2000 samples and the testing set consisted of 500 samples. Consequently, there were 40 training samples and 10 testing samples for each wood species. The PC1 and PC2 of the training and testing datasets were distributed as shown in Figure 11, where the distributions of both the training and testing sets were dispersed and uniform, indicating that the dataset was suitable for pattern classification.Figure 11
The 2D distribution of PC1 and PC2 for the training dataset in red color and the testing dataset in blue color: (a) VIS band; (b) NIR band.
(a)(b)


### 3.1. Comparisons with Conventional Algorithms

The fuzzy rule classifier was applied to the wood species spectral classification experiments and compared with other important classification schemes, such as the Bayes classifier (BC) [30], random forest (RF) [31], BP network (BPN) [32], SVM [33], and LeNet-5 [34]. The overall recognition accuracy (ORA) and processing speed for a testing sample from our testing dataset (i.e., time requirement, TR) are listed in Table 11. The computer configurations used are presented in Table 12. The ORA was calculated as follows (i.e., nright is the sample number correctly classified, and ntest is the total sample number of testing sets):(23)ORA=nrightntest.Table 11
Overall recognition accuracy (ORA) and time requirement (TR) comparisons of the testing dataset for different classifiers (ORA and TR refer to the mean values of 20 tests).
ModelDatasetORA (%)TR (ms)BCVIS (PCA7dim)76.200.050256‬NIR (PCA7dim)77.800.037920VIS (TSNE7dim)55.000.047946NIR (TSNE7dim)61.600.052136‬RFVIS (PCA7dim)83.802.437714NIR (PCA7dim)84.002.326404VIS (TSNE7dim)76.402.654658NIR (TSNE7dim)80.402.310316BPNVIS (PCA7dim)63.840.135030NIR (PCA7dim)61.480.117026VIS (TSNE7dim)54.040.123924NIR (TSNE7dim)60.800.140712LIBSVMVIS (PCA7dim)83.60 (linear)0.09293654.80 (RBF)0.123525NIR (PCA7dim)84.40 (linear)0.08189080.20 (RBF)0.131751VIS (TSNE7dim)72.40 (linear)0.08618423.80 (RBF)0.253162NIR (TSNE7dim)77.60 (linear)0.09152623.00 (RBF)0.211325LeNet-5VIS92.400.763721FRCVIS (PCA4dim)90.200.137274NIR (PCA4dim)92.920.141672VIS (TSNE4dim)71.880.159326NIR (TSNE4dim)81.120.173528D-S FRCVIS + NIR (PCA4dim)93.843.026516FW-D-S FRCVIS + NIR (PCA4dim)94.763.071578VIS: visible band; NIR: near-infrared band; FRC: fuzzy reasoning classifier; PCA: principal component analysis; BC: Bayes classifier; RF: random forest; BPN: BP network; CNN: convolutional neural network; LIBSVM: support vector machine; T-SNE: T-distributed stochastic neighbor embedding; D-S: Dempster–Shafer.Table 12
The configuration parameters of the computer used.
ConfigurationModelParameterCPUIntel I5-84006 core 6 thread, CPU clock speed 2.8 GHzRAMSamsung8 GB, DDR4 2800 MHzHard diskSamsung256 GB, SSD read: 470 MB/s, write: 473 MB/sIn the RF classification, the time complexity wasOm⋅ntest⋅d—where m is the feature dimension, d is the tree depth, and the RF number is 500. In the BP classification, the time complexity was Ontest⋅∑i=1d−1nini+1— where ni refers to the node number of the ith layer and d refers to the overall layer number, including the input and output layers. The structure of the BP network was 7 (input layer)-31 (hidden layer)-20 (output layer), and the transfer functions for the input and hidden layers were logsig and purelin, respectively. The BP network’s iteration times were 1000 with a target error and learning rate of 0.01. In the LeNet-5 classification, spectral dimension reduction was not used, whereas the spectral band 451–984 nm was used to form a 40×40 matrix. The training dataset was used to train a CNN with a structure comprising six convolution-2 pooling-12 convolution-2 pooling. The size of the convolution cores in the convolutional layers was 5, with a learning rate of 1 and training times of 1000. The time complexity was O∑i=1dMi2Ki2CiCi−1—where Mi is the size of the output feature image in the ith layer, Ki is the size of the convolution cores in the ith convolutional layer, Ci is the core number of the ith convolutional layer, and d is the overall convolutional layer number. In the SVM classification, a linear kernel function for the PCA algorithm and a radial basis function (RBF) for the T-SNE were used with a penalty factor of 1.2.In our fuzzy reasoning classifier (FRC) classification, we observed that the PCA algorithm performed much better than the T-SNE algorithm in terms of spectral dimension reduction. The best ORA of 96.3636% was achieved with our FRC, and the D-S decision-level fusion scheme was improved with the use of four PCs for the VIS band and six PCs for the NIR band, with a TR of 2.535915 ms for one testing sample.In other words, the RF algorithm could achieve good and efficient classification results using a large training dataset. However, its classification performance was poor with our small dataset—our training dataset only consisted of 2000 wood samples—and with low-dimensional feature vectors. Similarly, the BP neural network and LeNet-5 also required a large training dataset to complete network training. Regarding spectral dimension reduction, the classification results using our FRC and T-SNE were relatively poor compared with those of the PCA algorithm as the T-SNE is a nonlinear dimension reduction algorithm.


### 3.2. Comparisons with State-of-the-Art Algorithms

We compared the proposed scheme with other state-of-the-art wood species recognition schemes, all of which performed wood species classification using digital images of wood sample cross sections. We set up the image collection experimental equipment, as shown in Figure12, consisting of a charge-coupled device (CCD) camera, an optical microscope with a magnification ratio of 10–100, and a light-emitting diode (LED) light source. The wood color image selected was of size 1600×1200 pixels and magnification ratio 50. We used this imaging equipment to capture the cross-sectional color image of each wood sample so that each species included 50 images. This color image was then converted into a grayscale image of size 400×300pixels, although the color image was used in the CNN scheme. The computer configuration used is presented in Table 13, and the classification performance comparison is given in Table 14. We found that our FRC and improved D-S decision-level fusion scheme outperformed all other state-of-the-art classification schemes in terms of ORA.Figure 12
Our image-collective experimental equipment.Table 13
Computer configuration parameters.
ConfigurationModelParameterCPUIntel I7–9700F8 core 8 thread, CPU clock speed 3.00 GHzGPUNVIDIA GeForce8 GB, GDDR6 1650 MHzRTX 2060 SUPER2076 stream processorRAMCorsair Memory16 GB, DDR4 3000 MHZHard diskIntel256 GB, SSD read: 1570 MB/s, write 540 MB/sTable 14
Wood classification performance comparisons with state-of-the-art schemes.
ReferenceModelORA (%)[35]I-BGLAM72.32[36]LBP68.68[19, 37]SPPD7.32SPPD + I-BGLAM32.68Fuzzy + SPPD + BGLAM34.68[18]GA25.68GA + KDA29.00[38]VGG1683.36[39]SqueezeNet86.28[40]ResNet1894.40[41]GoogLeNet92.80[42]CNN83.00Our schemeFRC + improved D-S fusion94.76ORA: overall recognition accuracy; TR: time requirement; I-BGLAM: improved basic gray-level aura matrix; LBP: local binary pattern; SPPD: statistical property of pore distribution; GA: genetic algorithm; KDA: kernel discriminant analysis; CNN: convolutional neural network; FRC: fuzzy reasoning classifier; D-S: Dempster–Shafer.In these state-of-the-art wood species recognition schemes, Yusof et al. employed texture feature operators (e.g., basic gray-level aura matrix (BGLAM), improved basic gray-level aura matrix (I-BGLAM)), and pore distribution features (i.e., statistical properties of pores distribution (SPPD)) and several feature extraction algorithms, such as the genetic algorithm (GA) and kernel discriminant analysis (KDA) to classify more than 50 tropical wood species [18, 19, 35, 37]. However, their schemes were only suitable for the classification of hardwood species with pores. For softwood species without pores, the classification performance of their schemes was poor. Because our 50 wood species consist of both hardwood and softwood species, their schemes delivered poor classification results. Another texture feature operator, the local binary pattern (LBP), and a deep learning neural network were also used for classification comparisons [36, 38–42].


## 3.1. Comparisons with Conventional Algorithms

The fuzzy rule classifier was applied to the wood species spectral classification experiments and compared with other important classification schemes, such as the Bayes classifier (BC) [30], random forest (RF) [31], BP network (BPN) [32], SVM [33], and LeNet-5 [34]. The overall recognition accuracy (ORA) and processing speed for a testing sample from our testing dataset (i.e., time requirement, TR) are listed in Table 11. The computer configurations used are presented in Table 12. The ORA was calculated as follows (i.e., nright is the sample number correctly classified, and ntest is the total sample number of testing sets):(23)ORA=nrightntest.Table 11
Overall recognition accuracy (ORA) and time requirement (TR) comparisons of the testing dataset for different classifiers (ORA and TR refer to the mean values of 20 tests).
ModelDatasetORA (%)TR (ms)BCVIS (PCA7dim)76.200.050256‬NIR (PCA7dim)77.800.037920VIS (TSNE7dim)55.000.047946NIR (TSNE7dim)61.600.052136‬RFVIS (PCA7dim)83.802.437714NIR (PCA7dim)84.002.326404VIS (TSNE7dim)76.402.654658NIR (TSNE7dim)80.402.310316BPNVIS (PCA7dim)63.840.135030NIR (PCA7dim)61.480.117026VIS (TSNE7dim)54.040.123924NIR (TSNE7dim)60.800.140712LIBSVMVIS (PCA7dim)83.60 (linear)0.09293654.80 (RBF)0.123525NIR (PCA7dim)84.40 (linear)0.08189080.20 (RBF)0.131751VIS (TSNE7dim)72.40 (linear)0.08618423.80 (RBF)0.253162NIR (TSNE7dim)77.60 (linear)0.09152623.00 (RBF)0.211325LeNet-5VIS92.400.763721FRCVIS (PCA4dim)90.200.137274NIR (PCA4dim)92.920.141672VIS (TSNE4dim)71.880.159326NIR (TSNE4dim)81.120.173528D-S FRCVIS + NIR (PCA4dim)93.843.026516FW-D-S FRCVIS + NIR (PCA4dim)94.763.071578VIS: visible band; NIR: near-infrared band; FRC: fuzzy reasoning classifier; PCA: principal component analysis; BC: Bayes classifier; RF: random forest; BPN: BP network; CNN: convolutional neural network; LIBSVM: support vector machine; T-SNE: T-distributed stochastic neighbor embedding; D-S: Dempster–Shafer.Table 12
The configuration parameters of the computer used.
ConfigurationModelParameterCPUIntel I5-84006 core 6 thread, CPU clock speed 2.8 GHzRAMSamsung8 GB, DDR4 2800 MHzHard diskSamsung256 GB, SSD read: 470 MB/s, write: 473 MB/sIn the RF classification, the time complexity wasOm⋅ntest⋅d—where m is the feature dimension, d is the tree depth, and the RF number is 500. In the BP classification, the time complexity was Ontest⋅∑i=1d−1nini+1— where ni refers to the node number of the ith layer and d refers to the overall layer number, including the input and output layers. The structure of the BP network was 7 (input layer)-31 (hidden layer)-20 (output layer), and the transfer functions for the input and hidden layers were logsig and purelin, respectively. The BP network’s iteration times were 1000 with a target error and learning rate of 0.01. In the LeNet-5 classification, spectral dimension reduction was not used, whereas the spectral band 451–984 nm was used to form a 40×40 matrix. The training dataset was used to train a CNN with a structure comprising six convolution-2 pooling-12 convolution-2 pooling. The size of the convolution cores in the convolutional layers was 5, with a learning rate of 1 and training times of 1000. The time complexity was O∑i=1dMi2Ki2CiCi−1—where Mi is the size of the output feature image in the ith layer, Ki is the size of the convolution cores in the ith convolutional layer, Ci is the core number of the ith convolutional layer, and d is the overall convolutional layer number. In the SVM classification, a linear kernel function for the PCA algorithm and a radial basis function (RBF) for the T-SNE were used with a penalty factor of 1.2.In our fuzzy reasoning classifier (FRC) classification, we observed that the PCA algorithm performed much better than the T-SNE algorithm in terms of spectral dimension reduction. The best ORA of 96.3636% was achieved with our FRC, and the D-S decision-level fusion scheme was improved with the use of four PCs for the VIS band and six PCs for the NIR band, with a TR of 2.535915 ms for one testing sample.In other words, the RF algorithm could achieve good and efficient classification results using a large training dataset. However, its classification performance was poor with our small dataset—our training dataset only consisted of 2000 wood samples—and with low-dimensional feature vectors. Similarly, the BP neural network and LeNet-5 also required a large training dataset to complete network training. Regarding spectral dimension reduction, the classification results using our FRC and T-SNE were relatively poor compared with those of the PCA algorithm as the T-SNE is a nonlinear dimension reduction algorithm.


## 3.2. Comparisons with State-of-the-Art Algorithms

We compared the proposed scheme with other state-of-the-art wood species recognition schemes, all of which performed wood species classification using digital images of wood sample cross sections. We set up the image collection experimental equipment, as shown in Figure12, consisting of a charge-coupled device (CCD) camera, an optical microscope with a magnification ratio of 10–100, and a light-emitting diode (LED) light source. The wood color image selected was of size 1600×1200 pixels and magnification ratio 50. We used this imaging equipment to capture the cross-sectional color image of each wood sample so that each species included 50 images. This color image was then converted into a grayscale image of size 400×300pixels, although the color image was used in the CNN scheme. The computer configuration used is presented in Table 13, and the classification performance comparison is given in Table 14. We found that our FRC and improved D-S decision-level fusion scheme outperformed all other state-of-the-art classification schemes in terms of ORA.Figure 12
Our image-collective experimental equipment.Table 13
Computer configuration parameters.
ConfigurationModelParameterCPUIntel I7–9700F8 core 8 thread, CPU clock speed 3.00 GHzGPUNVIDIA GeForce8 GB, GDDR6 1650 MHzRTX 2060 SUPER2076 stream processorRAMCorsair Memory16 GB, DDR4 3000 MHZHard diskIntel256 GB, SSD read: 1570 MB/s, write 540 MB/sTable 14
Wood classification performance comparisons with state-of-the-art schemes.
ReferenceModelORA (%)[35]I-BGLAM72.32[36]LBP68.68[19, 37]SPPD7.32SPPD + I-BGLAM32.68Fuzzy + SPPD + BGLAM34.68[18]GA25.68GA + KDA29.00[38]VGG1683.36[39]SqueezeNet86.28[40]ResNet1894.40[41]GoogLeNet92.80[42]CNN83.00Our schemeFRC + improved D-S fusion94.76ORA: overall recognition accuracy; TR: time requirement; I-BGLAM: improved basic gray-level aura matrix; LBP: local binary pattern; SPPD: statistical property of pore distribution; GA: genetic algorithm; KDA: kernel discriminant analysis; CNN: convolutional neural network; FRC: fuzzy reasoning classifier; D-S: Dempster–Shafer.In these state-of-the-art wood species recognition schemes, Yusof et al. employed texture feature operators (e.g., basic gray-level aura matrix (BGLAM), improved basic gray-level aura matrix (I-BGLAM)), and pore distribution features (i.e., statistical properties of pores distribution (SPPD)) and several feature extraction algorithms, such as the genetic algorithm (GA) and kernel discriminant analysis (KDA) to classify more than 50 tropical wood species [18, 19, 35, 37]. However, their schemes were only suitable for the classification of hardwood species with pores. For softwood species without pores, the classification performance of their schemes was poor. Because our 50 wood species consist of both hardwood and softwood species, their schemes delivered poor classification results. Another texture feature operator, the local binary pattern (LBP), and a deep learning neural network were also used for classification comparisons [36, 38–42].


## 4. Conclusions

In this study, a novel wood species spectral classification scheme was proposed based on a fuzzy linguistic rule classifier and an improved decision-level fusion technique based on the D-S evidential theory. The VIS/NIR spectral reflectance curves of a wood sample’s cross section were measured using a USB 2000-VIS-NIR spectrometer and a FLAME-NIR spectrometer. As the VIS and NIR bands for the wood sample’s cross section have different spectral stabilities, they were processed using two different FRCs, and their classification results were further fused using an improved decision-level fusion technique based on the D-S evidential theory. The test results showed that the best ORA of our scheme reached 94.76% for 50 wood species, with little computational overhead.More generally, our scheme has the following advantages compared with existing wood species recognition schemes. First, the acquired wood spectral curves were usually noisy and variable because of the variability of the external environment—such as optical illumination intensity—and the wood sample’s internal factors—such as humidity, surface roughness, and intraspecies differences. The uncertainty of these wood spectral features could be resolved using fuzzy processing to some extent. Second, our scheme rapidly achieved good recognition results, particularly with small datasets, and the cost of the VIS/NIR spectrometer used was relatively low. The spectral dataset was a 1D signal set, which had a relatively low computational overhead compared to other 2D image datasets. Therefore, our scheme could be readily applied to wood recognition and classification in the industry in the near future.However, our scheme can only classify the known wood species which is included in our training dataset. In practical work, some unknown wood species samples may be encountered by our wood classification system. This issue is an unknown species identification problem under the open-world assumption, which can be solved in the certainty or uncertainty framework. For example, in an uncertainty framework, Tang et al. have proposed a new method for generation of generalized basic probability assignment (GBPA) based on evidence theory [43]. In this method, the maximum, minimum, and mean values were used to produce triangular fuzzy number of each class in different attributes, and the intersection points of test samples with triangular fuzzy numbers were calculated. Based on this method, it is feasible to produce a classifier which can effectively recognize the known and unknown classes. Therefore, we plan to investigate and improve this method for wood species classification, since the wood species quantity is greatly larger than the class quantity in [43]. On the other hand, in a certainty framework, we have also used a one-class classifier Support Vector Data Description (SVDD) [44], which can preclassify the wood samples into two categories (i.e., the known and unknown wood categories).



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*Source: 6088435-2021-07-23.xml*