# Fuzzy Multicriteria Decision-Making for Ranking Intercrop in Rubber Plantations under Social, Economic, and Environmental Criteria

Authors: Jitsupa Muangman; Kittipong Krootsong; Phattamon Polrong; Weera Yukunthorn; Weerawat Udomsap
Journal: Advances in Fuzzy Systems
 (2020)

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## Abstract

Rubber price instability causes great economic problems for rubber plantation in Thailand. Intercropping is an alternative way for rubber farmers in problem-solving. In this paper, we established decision-making system for plant selection in rubber fields under social, economic, and environment criteria with the use of fuzzy multicriteria decision-making (FMCDM) to rank plant options. Firstly, we modified the traditional FMCDM by defuzzification with norm centroid and developed the fuzzifier maps the norm centroid to triangular fuzzy number (TFN). According to fuzzification, the final rating evaluation of plant options are determined by total utility values. Finally, ranking of the plant options is obtained. Our modifications provided an alternative decision-making process with softer computational capability compared with the traditional method. In addition to soft computing, data visualization and analysis of the possibility in each factors could be investigated. This decision-making system was implemented in Phang-Nga Province, Thailand. Its outputs assisted the rubber farmer in selecting suitable plants for cultivation. Pros and cons of each plant options and area-based approaches were easily seen by data visualizations. This decision-making system provided beneficial information which support precision developments for rubber farmer and government agencies.


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## Body

## 1. Introduction

Rubber is one of the major crops cultivated in south of Thailand, and this is region possessed the largest area of rubber plantation [1]. Recently, fluctuation of rubber price affects farmer’s livelihoods. Intercropping of rubber tree plantations has been a strategy for earning higher incomes from the rubber crop [2]. The challenge of rubber intercropping in the 21st century is analysed considering not only physical environments but also socioeconomic and environments. So, plant selection under suitable area-based plantation conditions will be sustainable for rubber farming [3].The suitable plantation conditions could be determined by several criteria under social, economic, and environmental factors. MCDM is a mathematical tool with capability in importing both of qualitative and quantitative data. In addition, it is a powerful method for solving the complex decision problems. Applications of MCDM could be found in various fields such as business and management, economics, education, and agriculture [4–7]. Previously, MCDM had been applied on selecting intercrops in the rubber field under geographic criteria and economic criteria in Phitsanulok province, Thailand. They compared the use of analytical hierarchy process (AHP), the technique for order preference by similarity to ideal solution (TOPSIS), and the simple additive weighting (SAW) in computation [8].The computation of uncertain problems without observing the existence of events is well known as fuzzy set theory. An application of the fuzzy set couple to MCDM is to develop FMCDM and has been proved to be successful in several real-life problems [9]. In FMCDM, the linguistic data are evaluated in forms of fuzzy numbers. Ranking is performed using techniques of ordering fuzzy numbers [10–12]. The new techniques in computation are being currently developed, for example, using the FVK module in Excel [13] and using centroid of fuzzy numbers [14].Ranking with centroid is an interesting method according to the data collection of FMCDM analogous to the tensor model. If we use defuzzification technique with centroid norm of each fuzzy number, the tensor data would approach to the matrix of real numbers. So, this methodology is softer computing. This technique was developed by Chen in 1997 [15] for solving the tool steel-material selection problem under fuzzy environments [16]. The trapezoidal fuzzy number of the linguistic term is characterized by its centroid and ranked on simple arithmetic operations. It differs from the original problem which is computed on fuzzy arithmetic and is ranked by the total utility function as follows: let U be a fuzzy set; the utility of fuzzy number Ap=a1p,a2p,a3p is defined by(1)UAp=121+a3p−lu−l+a3p−a2p−u−a1pu−l+a2p−a1p,where l and u are infimum and supremum of membership functions.In fact, the trapezoidal fuzzy number (TrFN) of the rating scale was extended from TFN by repeating the core of fuzzy shape. For example, a very high level TFN (0.7,1,1) is extended to TrFN (0.7,1,1,1). By considering the use of centroid of TFN (0.7,1,1) = 0.9 and the centroid of TrFN (0.7,1,1,1) = 0.925, the squares are equal to 0.81 and 0.855625, respectively. We see that the multiplication of the best level would obtain the decreasing value. In this study, the improvement of multiplication of centroids and the development of computation for decision-making process including an investigation of the decision-making system in ordering intercrop rubber tree plantation under social, economic, and environmental criteria were established. This paper is organized as follows. In Section2, mathematical tools and computation on norm centroid of TFN are developed. The defuzzification-fuzzification technique was established for the ranking process with total utility values. In Section 3, the present decision making system for plant selection and ranking processing via FMCDM on norm centroid are discussed. In Section 4, we illustrate an application of decision-making system which provides recommendations to the rubber farmer, and the last section presents the conclusion and discussions relative to development and implementation of results.


## 2. Development of Mathematical Tools and Computation

In this section, we will develop fuzzy computing on the norm centroid. By considering the TFN used in this work, it is considered as a subset of0,13. Let x=x1,x2,x3 be a TFN such that x1≤x2≤x3 and let x and y be TFN, and the addition and multiplication are formulated as follows [13]:(2)Additionx+y=x1+y1,x2+y2,x3+y3,Multiplicationxy=x1y1,x2y2,x3y3.Based on the abovementioned computational method, one operation of the two TFNs corresponds to three operations of real numbers. Therefore, big TFN data yield a huge computing. To reduce the complexity of computation, the hard computing is replaced by a soft computing which is called the defuzzification method [14]. By this technique, one operation of the 2 TFNs corresponds to one operation of the centroid.


### 2.1. Modified Defuzzification and Significance

As mentioned previously, the multiplication of centroid reduces the level of decision-making. So, we will modify the defuzzification of linguistic terms by norm centroid in this section. Letx,y∈V⊂0,13 and t∈ℕ\1,2, a fuzzy norm ⊙t:V⟶0,1 is defined by(3)xt=x1+x3+t−2x2t.Centroid usage of linguistic terms in [15]is recalled. The linguistic terms associated with TFN a,b,c are extended to TrFN a,b,b,c and defuzzified with a+c+2b/4. It is obviously seen that the defuzzification is ⊙4. If we consider the confidence level at 100% = 1.0, then 95% = 0.95. We assume that the multiplication of centroids is about 0.95 which belongs to t=12. So, throughout this work, the use of ⊙12 has been implemented in our decision-making system. The five levels of importance are denoted as follows: NI: = not important, LI: = less important, OI: = ordinary important, I: = important, and VI: = very important. Similarly, the five levels of possibility are denoted as follows: I: = impossible, WP: = weak possibility, OP: = ordinary possibility, P: = possible, and SP: = strong possibility. The grey level is computed by RBG∗⊙12 as shown in Table 1.Table 1
Association between linguistic terms, fuzzy numbers, and their norms.The fuzzy norm of addition and multiplication is straightforward:(4)x+yt=xt+yt,(5)xyt=xtyt−Ex,y.To approximatexy12 by x12y12, the errors in Table 2 are verified by(6)Ex,y=x12y12−xy12.Table 2
Errors of multiplications.
E
x
,
y
NI/I
LI/WP
OI/OP
I/P
VI/SP
NI/I
0.00688
0.00521
0.00750
0.00729
0.00063
LI/WP
0.00521
0.01076
0.01250
0.01007
0.00729
OI/OP
0.00750
0.01250
0.01500
0.01250
0.00750
I/P
0.00729
0.01007
0.01250
0.01076
0.00521
VI/SP
0.00063
0.00729
0.00750
0.00521
0.00000Hence,∀x∈V∀y∈V,Ex,y<maxE⋅,⋅<5×10−2. Therefore, this method provides two significant digits.


### 2.2. Fuzzification

In the final state of traditional fuzzy MCDM, we applied (1) to the final rating fuzzy scores. So, we need to establish a fuzzifier which transforms the range of ⊙t to TFN. Figure 1 is considered, and let x1=x11,x21,x31 and x2=x12,x22,x32 be TFN of consecutive rating scale in V.Figure 1
Geometric representation of TFNs and their shapes.To construct the triangular shape ofx∗ from its norm, we consider the ratios of the lower and upper norms. Assume that x∗=x1∗,x2∗,x3∗, we get(7)xi∗−xi1xi2−xi1=x∗t−x1tx2t−x1t.Hence(8)xi∗=xi1+x∗t−x∗1x2t−x1txi2−xi1,for i=1,2,3.Suppose that we getx∗12=0.950625. From Table 1, P12<x∗12<SP12. By (8), we obtain(9)x1∗=0.5+0.950625−0.7083330.975−0.7083330.7−0.5=0.681719,x2∗=0.7+0.950625−0.7083330.975−0.7083331.0−0.7=0.972578,x3∗=1.0+0.950625−0.7083330.975−0.7083331.0−1.0=1.000000.Therefore,x∗=0.681719,0.972578,1.000000.


## 2.1. Modified Defuzzification and Significance

As mentioned previously, the multiplication of centroid reduces the level of decision-making. So, we will modify the defuzzification of linguistic terms by norm centroid in this section. Letx,y∈V⊂0,13 and t∈ℕ\1,2, a fuzzy norm ⊙t:V⟶0,1 is defined by(3)xt=x1+x3+t−2x2t.Centroid usage of linguistic terms in [15]is recalled. The linguistic terms associated with TFN a,b,c are extended to TrFN a,b,b,c and defuzzified with a+c+2b/4. It is obviously seen that the defuzzification is ⊙4. If we consider the confidence level at 100% = 1.0, then 95% = 0.95. We assume that the multiplication of centroids is about 0.95 which belongs to t=12. So, throughout this work, the use of ⊙12 has been implemented in our decision-making system. The five levels of importance are denoted as follows: NI: = not important, LI: = less important, OI: = ordinary important, I: = important, and VI: = very important. Similarly, the five levels of possibility are denoted as follows: I: = impossible, WP: = weak possibility, OP: = ordinary possibility, P: = possible, and SP: = strong possibility. The grey level is computed by RBG∗⊙12 as shown in Table 1.Table 1
Association between linguistic terms, fuzzy numbers, and their norms.The fuzzy norm of addition and multiplication is straightforward:(4)x+yt=xt+yt,(5)xyt=xtyt−Ex,y.To approximatexy12 by x12y12, the errors in Table 2 are verified by(6)Ex,y=x12y12−xy12.Table 2
Errors of multiplications.
E
x
,
y
NI/I
LI/WP
OI/OP
I/P
VI/SP
NI/I
0.00688
0.00521
0.00750
0.00729
0.00063
LI/WP
0.00521
0.01076
0.01250
0.01007
0.00729
OI/OP
0.00750
0.01250
0.01500
0.01250
0.00750
I/P
0.00729
0.01007
0.01250
0.01076
0.00521
VI/SP
0.00063
0.00729
0.00750
0.00521
0.00000Hence,∀x∈V∀y∈V,Ex,y<maxE⋅,⋅<5×10−2. Therefore, this method provides two significant digits.


## 2.2. Fuzzification

In the final state of traditional fuzzy MCDM, we applied (1) to the final rating fuzzy scores. So, we need to establish a fuzzifier which transforms the range of ⊙t to TFN. Figure 1 is considered, and let x1=x11,x21,x31 and x2=x12,x22,x32 be TFN of consecutive rating scale in V.Figure 1
Geometric representation of TFNs and their shapes.To construct the triangular shape ofx∗ from its norm, we consider the ratios of the lower and upper norms. Assume that x∗=x1∗,x2∗,x3∗, we get(7)xi∗−xi1xi2−xi1=x∗t−x1tx2t−x1t.Hence(8)xi∗=xi1+x∗t−x∗1x2t−x1txi2−xi1,for i=1,2,3.Suppose that we getx∗12=0.950625. From Table 1, P12<x∗12<SP12. By (8), we obtain(9)x1∗=0.5+0.950625−0.7083330.975−0.7083330.7−0.5=0.681719,x2∗=0.7+0.950625−0.7083330.975−0.7083331.0−0.7=0.972578,x3∗=1.0+0.950625−0.7083330.975−0.7083331.0−1.0=1.000000.Therefore,x∗=0.681719,0.972578,1.000000.


## 3. Materials and Methods

The traditional MCDM in Figure2 consists of five steps. Step 1: problem situation, step 2: assign weight, step 3: assign rating, step 4: aggregating ratings, and step 5: ranking.Figure 2
Framework of decision-making process.


### 3.1. Problem Situation and Data Collection

In the generalized decision-making of selecting offered choices, we suppose that there arep ways and the suitability indicators possessed q criteria. The evaluations of r decision-makers consisted of 2 parts: (1) importance of criteria and (2) possibility of the choices in each criteria. Both evaluations provided 2 fuzzy matrices, called weighting fuzzy matrix and rating fuzzy matrix.LetS be a set of rating scales in Table 1. For i=1,2,…,q and j=1,2,…,r, the weighting fuzzy matrix could be written as W=wij, where wij∈S are the weight of ith criteria, evaluated by jth expert. The rating fuzzy matrix R=Rij, for i=1,2,…,p and j=1,2,…,q. Note that Rij∈S are the rating of the choices, evaluated by decision-makers. Here, we see that R is a p×q matrix and W is a q×r matrix.


### 3.2. Application on FMCDM

The final ratingF in traditional FMCDM for i=1,2,…,p is computed as follows:(10)F=Fi=1q∑j=1qRijW¯j=1q∑j=1qRij1r∑k=1rwjk=1qr∑k=1r∑j=1qRijwjk.Then, we apply total utility function to the fuzzy setF1,F2,…,Fp. Consequently, the ranking of the choices would be obtained. Now, we will apply our method on FMCDM. Let Wt be matrix of ⊙t of each element in W, that is, Wt=wijtij. Likewise, Rt=Rijtij. Consider Ft by the implication of laws (10) and (5):(11)Ft=1q∑j=1qRijW¯jt=1qr∑k=1r∑j=1qRijwjkt.Applying (4) and then approximating with (5), we get(12)Ft=1qr∑j=1qRijwjkt≈1qr∑k=1r∑j=1qRijtijwjktjk=1r∑k=1rRtWtik.Finally, we apply defuzzification toFt. The final rating fuzzy matrix for indicating total utility of each choice is obtained. The procedure of computation is represented Figure 3.Figure 3
Computational network of FMCDM.


### 3.3. Ordering the Optimal Intercrop Rubber Tree Plantations

Next, we will demonstrate the implementation and illustrate a case study in Phang-Nga province, Thailand.Step 1. Problem situation: in a case study of ordering intercrop rubber tree, 3 experts were required (r=3); all experts are professionals in the agricultural society (D1), agricultural economics (D2), and agricultural environment (D3). The selected plants consisted of 5 choices (p=5) including Robusta coffee (A1), Baegu (A2), Manpu (A3), Chaya (A4), and White Turmeric (A5). A total of 25 criteria (q=25) [17–21] were categorized into 3 including social, economic, and environment viewpoints (Table 3).Step 2. Data collections and their visualizationsStep 2.1. Weighting criteria by the experts: we assign weighting criteria to the experts, and the levels of importance of each criterion are shown in Tables 4–6, associated with social, economic, and environmental viewpoints, respectively.By applying results in Table1, the above data represent visualization, as shown in Table 7.Step 2.2 . Rating scales by rubber farmers: we assign rating scales evaluation of each plant under all criteria to the farmer, and the results are shown in Tables 8–10. The visualization in Table 11 shows the possibility of cropping under the each criteria.Step 3. Final rating: the final defuzzification score in Table 12 is computed by using (12)Step 4. Ranking: finally, the fuzziness was taken as the average of the defuzzification score of each plant in Table 12 by fuzzy rule (4). The ranking is obtained by indicating fuzzification of each plant with the total utility function. The results of this step are shown in Table 13.Table 3
List of criteria of the decision-making process.
Criteria
Social
Meaning
C01
Cropping
C02
Harvesting
C03
Marketing
C04
Knowledge management
C05
Collective farming
C06
Government support
Economic
C07
Investment
C08
Low cost
C09
Return
C10
Market need
C11
Noncompetition market
C12
Low price risk
C13
Low production risk
Environment
C14
Primary soil nutrient
C15
Secondary and microsoil nutrient
C16
Bulk density of soil
C17
Soil texture
C18
Soil PH
C19
Soil temperature
C20
Light intensity
C21
Rain
C22
Wetland
C23
Temperature
C24
Stable climate
C25
LandscapeTable 4
Linguistic terms of experts’ viewpoint in social criteria.
D1
D2
D3
C01
OI
VI
OI
C02
VI
I
VI
C03
VI
I
VI
C04
I
OI
OI
C05
VI
OI
I
C06
VI
OI
ITable 5
Linguistic terms of expert’ viewpoint in economic criteria.
D1
D2
D3
C07
LI
I
OI
C08
LI
I
LI
C09
VI
I
I
C10
VI
VI
VI
C11
NI
I
NI
C12
I
I
OI
C13
LI
I
LITable 6
Linguistic terms of experts’ viewpoint in environmental criteria.
D1
D2
D3
C14
VI
VI
VI
C15
OI
OI
LI
C16
NI
I
NI
C17
NI
LI
LI
C18
I
OI
OI
C19
NI
NI
LI
C20
I
I
I
C21
I
I
VI
C22
NI
NI
NI
C23
NI
NI
NI
C24
NI
NI
LI
C25
VI
LI
LITable 7
Visualization of weighting by experts.Table 8
Linguistic terms of the decision-maker’s viewpoint in social criteria.
A1
A2
A3
A4
A5
C01
IP
P
P
IP
P
C02
IP
P
SP
WP
SP
C03
P
SP
P
WP
OP
C04
OP
P
P
WP
P
C05
P
WP
IP
IP
WP
C06
WP
OP
WP
IP
WPTable 9
Linguistic terms of decision-maker’s viewpoint in economic criteria.
A1
A2
A3
A4
A5
C07
P
WP
IP
IP
IP
C08
P
WP
IP
WP
IP
C09
P
SP
SP
P
OP
C10
SP
SP
OP
IP
IP
C11
IP
IP
OP
WP
IP
C12
WP
P
P
P
OP
C13
OP
IP
WP
OP
OPTable 10
Linguistic terms of decision-maker’s viewpoint in environment criteria.
A1
A2
A3
A4
A5
C14
P
SP
SP
P
P
C15
OP
P
P
P
OP
C16
SP
SP
SP
SP
SP
C17
P
SP
SP
SP
OP
C18
P
P
P
P
P
C19
OP
OP
OP
OP
OP
C20
P
OP
OP
P
P
C21
OP
P
P
OP
OP
C22
P
P
P
P
P
C23
OP
P
P
OP
OP
C24
OP
SP
SP
OP
WP
C25
OP
SP
P
OP
OPTable 11
Visualization of decision-maker ratings.Table 12
Defuzzification score.
D1
D2
D3
A1
0.293889
0.303083
0.274792
A2
0.383367
0.362844
0.350381
A3
0.333281
0.337611
0.310428
A4
0.211708
0.234089
0.196422
A5
0.2705
0.268169
0.244458Table 13
Ranking process.
Choices
Average defuzzified value
Fuzzification
Total utility
Ranking
Lower
Core
Upper
A1
0.290588
0
0.298786
0.499191
0.474425
3
A2
0.365531
0.070909
0.370909
0.606364
0.564765
1
A3
0.327106
0.034022
0.334022
0.551033
0.518884
2
A4
0.214073
0
0.212707
0.441805
0.394254
5
A5
0.261043
0
0.265548
0.477032
0.443918
4In a case study, Tables7, 11, 12, and 13 presented useful information for analysis and providing recommendations. The visualization of weighting by the experts in Table 7 showed that the environmental factor was found to be less important compared with other factors, as shown in the intensity of colouring. It was satisfying based on the fact that Phang-Nga province could be regarded as an agricultural land. The cons of the rubber farmer was demonstrated in Table 11. It is said that the rubber farmer felts concerned and lacked of confidence on agricultural economics of all plants except for Robusta coffee. However, in terms of social agriculture, agriculture practices and management of Robusta coffee were found to be problematic. According to the relationship of plant options and criteria represented in Table 12, (row views), interesting results in terms of economic viewpoints were found in Robusta coffee and chaya, whilst other plants were found to be interesting in social agriculture viewpoints. On column views, the best plant option in terms of social, economic, and environmental criteria is Baegu. And lastly, the table provides results on ranking of suitable plant options for the rubber farmer.


## 3.1. Problem Situation and Data Collection

In the generalized decision-making of selecting offered choices, we suppose that there arep ways and the suitability indicators possessed q criteria. The evaluations of r decision-makers consisted of 2 parts: (1) importance of criteria and (2) possibility of the choices in each criteria. Both evaluations provided 2 fuzzy matrices, called weighting fuzzy matrix and rating fuzzy matrix.LetS be a set of rating scales in Table 1. For i=1,2,…,q and j=1,2,…,r, the weighting fuzzy matrix could be written as W=wij, where wij∈S are the weight of ith criteria, evaluated by jth expert. The rating fuzzy matrix R=Rij, for i=1,2,…,p and j=1,2,…,q. Note that Rij∈S are the rating of the choices, evaluated by decision-makers. Here, we see that R is a p×q matrix and W is a q×r matrix.


## 3.2. Application on FMCDM

The final ratingF in traditional FMCDM for i=1,2,…,p is computed as follows:(10)F=Fi=1q∑j=1qRijW¯j=1q∑j=1qRij1r∑k=1rwjk=1qr∑k=1r∑j=1qRijwjk.Then, we apply total utility function to the fuzzy setF1,F2,…,Fp. Consequently, the ranking of the choices would be obtained. Now, we will apply our method on FMCDM. Let Wt be matrix of ⊙t of each element in W, that is, Wt=wijtij. Likewise, Rt=Rijtij. Consider Ft by the implication of laws (10) and (5):(11)Ft=1q∑j=1qRijW¯jt=1qr∑k=1r∑j=1qRijwjkt.Applying (4) and then approximating with (5), we get(12)Ft=1qr∑j=1qRijwjkt≈1qr∑k=1r∑j=1qRijtijwjktjk=1r∑k=1rRtWtik.Finally, we apply defuzzification toFt. The final rating fuzzy matrix for indicating total utility of each choice is obtained. The procedure of computation is represented Figure 3.Figure 3
Computational network of FMCDM.


## 3.3. Ordering the Optimal Intercrop Rubber Tree Plantations

Next, we will demonstrate the implementation and illustrate a case study in Phang-Nga province, Thailand.Step 1. Problem situation: in a case study of ordering intercrop rubber tree, 3 experts were required (r=3); all experts are professionals in the agricultural society (D1), agricultural economics (D2), and agricultural environment (D3). The selected plants consisted of 5 choices (p=5) including Robusta coffee (A1), Baegu (A2), Manpu (A3), Chaya (A4), and White Turmeric (A5). A total of 25 criteria (q=25) [17–21] were categorized into 3 including social, economic, and environment viewpoints (Table 3).Step 2. Data collections and their visualizationsStep 2.1. Weighting criteria by the experts: we assign weighting criteria to the experts, and the levels of importance of each criterion are shown in Tables 4–6, associated with social, economic, and environmental viewpoints, respectively.By applying results in Table1, the above data represent visualization, as shown in Table 7.Step 2.2 . Rating scales by rubber farmers: we assign rating scales evaluation of each plant under all criteria to the farmer, and the results are shown in Tables 8–10. The visualization in Table 11 shows the possibility of cropping under the each criteria.Step 3. Final rating: the final defuzzification score in Table 12 is computed by using (12)Step 4. Ranking: finally, the fuzziness was taken as the average of the defuzzification score of each plant in Table 12 by fuzzy rule (4). The ranking is obtained by indicating fuzzification of each plant with the total utility function. The results of this step are shown in Table 13.Table 3
List of criteria of the decision-making process.
Criteria
Social
Meaning
C01
Cropping
C02
Harvesting
C03
Marketing
C04
Knowledge management
C05
Collective farming
C06
Government support
Economic
C07
Investment
C08
Low cost
C09
Return
C10
Market need
C11
Noncompetition market
C12
Low price risk
C13
Low production risk
Environment
C14
Primary soil nutrient
C15
Secondary and microsoil nutrient
C16
Bulk density of soil
C17
Soil texture
C18
Soil PH
C19
Soil temperature
C20
Light intensity
C21
Rain
C22
Wetland
C23
Temperature
C24
Stable climate
C25
LandscapeTable 4
Linguistic terms of experts’ viewpoint in social criteria.
D1
D2
D3
C01
OI
VI
OI
C02
VI
I
VI
C03
VI
I
VI
C04
I
OI
OI
C05
VI
OI
I
C06
VI
OI
ITable 5
Linguistic terms of expert’ viewpoint in economic criteria.
D1
D2
D3
C07
LI
I
OI
C08
LI
I
LI
C09
VI
I
I
C10
VI
VI
VI
C11
NI
I
NI
C12
I
I
OI
C13
LI
I
LITable 6
Linguistic terms of experts’ viewpoint in environmental criteria.
D1
D2
D3
C14
VI
VI
VI
C15
OI
OI
LI
C16
NI
I
NI
C17
NI
LI
LI
C18
I
OI
OI
C19
NI
NI
LI
C20
I
I
I
C21
I
I
VI
C22
NI
NI
NI
C23
NI
NI
NI
C24
NI
NI
LI
C25
VI
LI
LITable 7
Visualization of weighting by experts.Table 8
Linguistic terms of the decision-maker’s viewpoint in social criteria.
A1
A2
A3
A4
A5
C01
IP
P
P
IP
P
C02
IP
P
SP
WP
SP
C03
P
SP
P
WP
OP
C04
OP
P
P
WP
P
C05
P
WP
IP
IP
WP
C06
WP
OP
WP
IP
WPTable 9
Linguistic terms of decision-maker’s viewpoint in economic criteria.
A1
A2
A3
A4
A5
C07
P
WP
IP
IP
IP
C08
P
WP
IP
WP
IP
C09
P
SP
SP
P
OP
C10
SP
SP
OP
IP
IP
C11
IP
IP
OP
WP
IP
C12
WP
P
P
P
OP
C13
OP
IP
WP
OP
OPTable 10
Linguistic terms of decision-maker’s viewpoint in environment criteria.
A1
A2
A3
A4
A5
C14
P
SP
SP
P
P
C15
OP
P
P
P
OP
C16
SP
SP
SP
SP
SP
C17
P
SP
SP
SP
OP
C18
P
P
P
P
P
C19
OP
OP
OP
OP
OP
C20
P
OP
OP
P
P
C21
OP
P
P
OP
OP
C22
P
P
P
P
P
C23
OP
P
P
OP
OP
C24
OP
SP
SP
OP
WP
C25
OP
SP
P
OP
OPTable 11
Visualization of decision-maker ratings.Table 12
Defuzzification score.
D1
D2
D3
A1
0.293889
0.303083
0.274792
A2
0.383367
0.362844
0.350381
A3
0.333281
0.337611
0.310428
A4
0.211708
0.234089
0.196422
A5
0.2705
0.268169
0.244458Table 13
Ranking process.
Choices
Average defuzzified value
Fuzzification
Total utility
Ranking
Lower
Core
Upper
A1
0.290588
0
0.298786
0.499191
0.474425
3
A2
0.365531
0.070909
0.370909
0.606364
0.564765
1
A3
0.327106
0.034022
0.334022
0.551033
0.518884
2
A4
0.214073
0
0.212707
0.441805
0.394254
5
A5
0.261043
0
0.265548
0.477032
0.443918
4In a case study, Tables7, 11, 12, and 13 presented useful information for analysis and providing recommendations. The visualization of weighting by the experts in Table 7 showed that the environmental factor was found to be less important compared with other factors, as shown in the intensity of colouring. It was satisfying based on the fact that Phang-Nga province could be regarded as an agricultural land. The cons of the rubber farmer was demonstrated in Table 11. It is said that the rubber farmer felts concerned and lacked of confidence on agricultural economics of all plants except for Robusta coffee. However, in terms of social agriculture, agriculture practices and management of Robusta coffee were found to be problematic. According to the relationship of plant options and criteria represented in Table 12, (row views), interesting results in terms of economic viewpoints were found in Robusta coffee and chaya, whilst other plants were found to be interesting in social agriculture viewpoints. On column views, the best plant option in terms of social, economic, and environmental criteria is Baegu. And lastly, the table provides results on ranking of suitable plant options for the rubber farmer.


## 4. Conclusions

The decision-making system for intercrop selection in the rubber field was investigated in particular for the rubber famer in the area. According to general information of experts admitted in the system, all of them resided in the local area. In the analysis, the experts verified area-based criteria based on social, economic, and environmental viewpoints and evaluated the level of importance of each criterion. Next, the rubber farmers listed plants based on interests and evaluated the possibility of each plant in each criterion. The results of the system were reported to be suitable for individuals; the input data were quite vague represented in forms of five fuzzy rating scales and defuzzified by fuzzy norm. Our mathematical objects were transformed from fuzzy space to real space. Moreover, the data of weighting criteria (importance) and rating alternative plants (possibility) could be visualized by colouring defuzzified values. Finally, we used the fuzzification technique and applied total utility function. The ranking of the plants was determined to support the farmer’s decision-making. Hence, the complexity of computation was reduced by the defuzzification-fuzzification technique.By the implementation of the results of from our decision-making system for problem-solving in ordering the optimal intercrop rubber tree plantations under social, economic,, and environment criteria in Klongkean, Phang-Nga province, Thailand, we get the ranking as follows: Baegu, Manpu, Robusta coffee, White Turmeric, and Chaya, respectively. The decision-maker (rubber farmer) agrees to the results based on the popularity of Baegu and Manpu in local area. However, Baegu was found to possess more advantages compared with Manpu in terms of commercials. Chaya was seen as a new plant for the farmer in the local area. Some farmers might find this plant interesting, but the lack of knowledge in farm management and marketing caused Chaya to be considered as the worst choice. On the whole, not only do the rubber farmer gains benefit from the decision-making system but also government agencies and local authorities. Sufficient area-based data from rubber farmers could provide information supporting further development, and development plans could literally result in sustainable rubber intercropping. By considering some limitations, it should be acknowledged that the created decision-making system could provide recommendations and resolutions for local problems and the ranking is compatible to the individual rubber farmers; it could not be generalized to all local or global rubber farmers. For further studies, it would be more beneficial to develop the decision-making software based on various platforms so that the future decision-making system could be adapted to handle with other problems occurring with individual resolutions, e.g., suitable educational program for individual students.



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*Source: 6508590-2020-05-08.xml*