# Brain Tumor Detection using Decision-Based Fusion Empowered with Fuzzy Logic

Authors: Aqsa Tahir; Muhammad Asif; Maaz Bin Ahmad; Toqeer Mahmood; Muhammad Adnan Khan; Mushtaq Ali
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Brain tumor is regarded as one of the fatal and dangerous diseases on the planet. It is present in the form of uncontrolled and irregular cells in the brain of an infected individual. Around 60% of glioblastomas turn into large tumors if it is not diagnosed earlier. Some valuable literature is available on tumor diagnosis, but there is room for improvement in overall performance. Machine Learning (ML)-based techniques have been widely used in the medical domain for early diagnostic diseases. The use of ML techniques in conjunction with improved image-guided technology may help in improving the performance of the brain tumor detection process. In this work, an ML-based brain tumor detection technique is presented. Adaptive Back Propagation Neural Network (ABPNN) and Support Vector Machine (SVM) algorithms are used along with fuzzy logic. The fuzzy logic is used to fuse the result of ABPNN and SVM. The proposed technique is developed using the BRATS dataset. Experimental results reveal that the ABPNN model achieved 98.67% accuracy in the training phase and 96.72% accuracy in the testing phase. On the other hand, the SVM model has attained 98.48% and 97.70% accuracy during the training and testing phases. After applying fuzzy logic for decision-based fusion, the overall accuracy of the proposed technique reaches 98.79% and 97.81% for the training and the testing phases, respectively. The comparative analysis with existing techniques shows the supremacy of the proposed technique.


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## Body

## 1. Introduction

The term “tumor” refers to a disease that causes swelling or corpus in the body. It can be related to any pathological process. Tumors constitute a significant demonstration of a massive and diverse clutch of ailments known as cancers or usually neoplasms [1]. The brain tumor is one of the fatal and complex types of tumor. It is formed because of a remarkable and aberrant increase in the cells inside the human brain. In ordinary circumstances, the development of a tumor initiates from the blood vessels, cells of the brain, and nerves imminent out of the brain. Over time, the brain tumor has become a significant cause of disabilities and deaths worldwide [2, 3]. Brain tumor location and its capability to feast rapidly make treatment with radiations or surgery alike fighting an opponent hiding amongst caves and minefields. Inappropriately, many safer and easier ways to eliminate a small tumor than a large one are available [4]. About 60% of glioblastomas start as lower small tumors and, over time, become giant tumors.According to the United States (US), National Cancer Institute estimated new brain tumor cases in the year 2022 are 25,050 (14,170 men and 10,880 women), and estimated deaths caused by brain tumors will be 18,280 [5]. It is also expected that 4,170 children (less than 15 years) will also be affected by a brain tumor. Worldwide, an estimated 308,102 primary brain or spinal cord tumor cases will be reported in 2020. Figure 1 shows the rate of new cases and death rate due to brain tumors in the US.Figure 1
Number of brain tumor cases per year in the US [5].Figure2 shows the overall age groupwise number of cases. As it shows, brain tumor cases are high in people aged 60–75. These are moderate in people aged 45–60 and 75–80. Moreover, these are minor in people under 45 and major in people above 80.Figure 2
Number of brain tumor cases per age group [6].In medical science, technology helps scientists examine diseases on a cellular level. It provides antibodies against them in the early stage, which will help to save thousands of lives all-round the globe. Early detection of a brain tumor may help to reduce the casualty rate of brain tumor patients. The brain tumor manual diagnostic procedure is done with the help of domain specialists, which is an extraordinary time taking task. The detection accuracy is highly dependent on the expertise of the domain specialist. Artificial intelligence has brought a revolution in the medical diagnostic domain, improving efficiency and accuracy. The use of ML-based techniques for brain tumor detection may help to speed up the diagnosis process and reduce the death rate. There are some valuable ML-based techniques in the literature for brain tumor detection, but there is room to improve the overall accuracy of these techniques.This paper presents a brain tumor detection technique in which Adaptive Back Propagation Neural Network (ABPNN) and Support Vector Machine (SVM) algorithms are used along with fuzzy logic. The fuzzy logic is used to fuse the result of ABPNN and SVM, which may help to reduce the false diagnosis. The dataset used in this work to develop the technique is taken from the Kaggle website [7]. It contains Computed tomography (CT) scan details of 3762 patients. It comprises 17 input parameters and one output parameter [7]. The experimental results show that the overall accuracy of the proposed technique is 98.79% and 97.81% for the training and the testing phases, respectively.The rest of the article is organized as follows. Section2 presents the literature review in which different methodologies and results are discussed. In Section 3, the proposed methodology is explained. Section 4 describes the experimental results and comparative analysis. Lastly, the paper is concluded in Section 5.


## 2. Literature Review

Digital image processing and computer vision are playing a vital role in many applications such as remote sensing, autonomous driving, medical image analysis, pose detection, security-based applications, and automated disease detection [8–12]. Recent focus of computer vision community is the use of deep-learning model [13–15] that are computationally expensive. However, at the same time, the research community is still widely presenting machine learning (ML)-based solutions [16–18].In the literature, several attempts have been made to diagnose brain tumors using various ML techniques. Babu et al. [19] have presented a fusion-based brain tumor segmentation technique in which a convolutional neural network (CNN) is used for the fusion of Chan-Vese and level set segmentation methods. They also performed a comparative analysis of fusion-based and clustered-based segmentation techniques to identify the tumor. They claimed that CNN fusion-based segmentation outperforms the clustered-based segmentation technique in terms of segmentation error and minimal loss of information. Abbas et al. [20] have explained Local Independent Projection-based Classification (LIPC) for tumor segmentation using Principal Component Analysis (PCA). Image enhancement and noise removal are done using image preprocessing. To achieve an enhanced and efficient classification score, different textural features are considered and condensed using PCA. The segmentation results demonstrated a 0.95 Dice Score (DS) and 0.72 precision.Rajan & Sundar [21] have proposed a hybrid-energy-efficient technique for automatic brain tumor segmentation and detection. They used Support Vector Machine (SVM) for brain tumor detection and K-means clustering with Fuzzy C-Means and active contours to perform brain tumor segmentation. They have attained an accuracy of 97.73%. The main limitation of their model is its high computational time because of the numerous techniques involved. Ullah et al. [22] have proposed a brain MRI image classification technique that classifies images into abnormal and normal classes. After performing several preprocessing steps, they used Discrete Wavelet Transform (DWT) for feature extraction. Finally, they used an advanced Deep Neural Network (DNN) to classify whether the brain MRI image is normal or abnormal. They have achieved 95.8% accuracy. Josephine & Murugan [23] have proposed a method for detecting brain cancer utilizing Artificial Neural networks (ANN). They used Gabor features, Gray Level Co-occurrence Matrix (GLCM), and associated texture feature for brain tumor detection. They achieved 96% accuracy on a dataset of 30 MRI images. Ahmmed et al. [24] have proposed a technique for a brain tumor and its stages classification based on SVM and ANN. They used Temper-based K-means and modified Fuzzy C-means (TKFCM) clustering algorithm for segmentation of MRI images. Region property-based features and first-order statistics are extracted from segmented images. The first-order statistic is used to detect tumors from MRI images with the help of SVM. The contrast, the second type of feature helps to detect the stage of the tumor using the ANN. They have achieved an accuracy of 97.37% with a Bit Error Rate (BER) of 0.0294.Mehmood et al. [6] have proposed a system to assist medical specialists that have the capabilities to perform brain tumor detection, segmentation, and 3D visualization from MRI images. For segmentation, they have used semiautomatic and adaptive threshold selection procedures. To classify a tumor into benign and malignant, the SVM classification model is used. Lastly, the volume marching cube algorithm is used for 3D visualization of the brain and tumors. They have achieved 99% accuracy. Dutta & Bandyopadhyay [25] have proposed a brain tumor detection technique using NGBoost classifier. The authors claimed an accuracy of 98.54%. Dutta & Bandyopadhyay [26] have proposed a technique for brain tumor detection using AdaBoost classifier. They have attained an accuracy of 98.97%. Tahir et al. [27] have proposed a technique for brain tumor detection. They have attained an accuracy of 87%. Munajat & Utaminingrum [28] have presented a GLCM and Back-Propagation Neural Network (BPNN)-based technique for brain tumor detection. They attained an accuracy of 88.03% with an average computation time of 0.601 sec. Ismael & Abdel-Qader [29] have presented a brain tumor detection framework that uses statistical features along with a neural network algorithm. To compute the statistical features, the 2D Gabor filter and 2D DWT are used. The authors claimed 91.9% accuracy for all types of tumors and a specificity of 96% for Meningioma, 96.29% for Glioma, and 96.29% for Pituitary tumors.Amin et al. [30] have developed an unsupervised clustering method for the segmentation of tumors. A Fused Feature Vector (FFV) is used which is a combination of the Local Binary Pattern (LBP), Gabor Wavelet Features (GWF), segmentation-based fractal texture analysis (SFTA) components, and the histogram of oriented gradients. The classification of tumors among three subtumoral regions is done using Random Forest (RF) classifier. To avoid the overfitting problem, 0.5 holdout cross-validation and five-fold methodologies are applied and detected tumors with reasonable confidence having 100% sensitivity. Ibrahim et al. [31] have developed a neural network-based technique for brain tumor detection through MRI images. It consists of three phases including preprocessing, dimensionality reduction, and classification. The experimental analysis shows that they attained an accuracy of 96.33%. Othman & Basri [32] have designed an automated brain tumor classification technique using PCA and Probabilistic Neural Network (PNN). They used PCA for dimensionality reduction and PNN for classification. The outcomes displayed that the proposed framework accomplished 73% correctness. Najadat et al. [33] have developed a decision tree classifier to recognize anomalies in CT brain pictures. They have achieved an accuracy of 88% on the training set and 58% on 2-fold validation. Balafar et al. [34] have presented a review of brain tumor segmentation techniques. They covered imaging modalities, noise reduction techniques, inhomogeneity correction, magnetic resonance imaging, and segmentation.Although several valuable studies on brain tumor diagnosis and segmentation using different ML techniques have been proposed, most of these are developed using a limited number of images and have room for improvement in overall performance as explained in Table1. Therefore, an efficient and accurate technique needs to be developed on a large dataset for diagnosing brain tumors.Table 1
Summary of existing work.
AuthorsTechniquesDatasetRemarksBabu et al. [19]CNN fusion followed by Chan-Veseactive contour-based segmentationDS 1-BRATS 2015and DS 2-brain webThe CNN fusion-based segmentation is better than clustered-basedsegmentation for brain tumor detection in termsof segmentation error and minimal loss of informationAbbas et al. [20]PCA and LIPCMICCAI dataset 30 imagesThey have performed segmentation with 0.95 DS and 0.72 precisionRajan & Sundar [21]SVM, K-means clustering withfuzzy C-means and active contours41 imagesThey have attained an accuracy of 97.73%.The main limitation of this model is high computational complexityUllah et al. [22]DWT and DNN71 imagesThey have attained an accuracy of 95.8%Josephine & Murugan [23]Artificial neural network30 imagesThey have achieved 96% accuracyAhmmed et al. [24]TKFCM, SVM, ANN46 imagesThey have achieved 97.37% accuracy with 0.0294 BERMehmood et al. [6]SVM and volumemarching cube algorithm256 imagesThey have achieved 99% accuracyDutta & Bandyopadhyay [25]NGBoost1644 imagesThey have attained an accuracy of 98.54%Dutta & Bandyopadhyay [26]AdaBoost1644 imagesThey have attained an accuracy of 98.97%Munajat & Utaminingrum [28]BPNN3762 imagesThey have attained an accuracy of 88.03%Ismael & Abdel-Qader [29]2D DWT, 2D gabor filter andback-propagation neural network3064 slicesThey have obtained 91.9% accuracy for all types of tumorsand a specificity of 96% for meningioma, 96.29% for gliomaand 96.29% for pituitary tumors correspondinglyAmin et al. [30]RF along with GWF HOG,LBP, and SFTA features531 imagesThey have claimed 100% sensitivityIbrahim et al. [31]PCA and BPNN174 imagesThey have attained 96.33% accuracyOthman & Basri [32]PCA and PNN35 imagesThey have obtained 73% accuracyNajadat et al. [33]Precision tree classifier and ABPNN25 imagesThey have achieved 59% accuracy


## 3. Proposed Method

This work uses ABPNN and SVM techniques along with fuzzy logic to develop a brain tumor diagnosis system. Figure3 shows a block diagram of the proposed system. It consists of training and validation phases. The training phase is divided into three layers; data acquisition, preprocessing, and application. In the data acquisition layer, the BRATS dataset is taken from the Kaggle website [7]. It contains Computed Tomography (CT) scan details of 3762 patients. It comprises 17 input parameters and one output parameter that indicates an abnormal or healthy person [7]. Table 2 lists the attributes of the dataset.Figure 3
Block diagram of the proposed system.Table 2
Input and output variables of the proposed DBFEFL system model.
Sr. NoInput/output variable nameInp-1MeanInp-2VarianceInp-3Standard deviationInp-4SkewnessInp-5KurtosisInp-6ContrastInp-7EnergyInp-8(ASM)Inp-9EntropyInp-10HomogeneityInp-11DissimilarityInp-12CorrelationInp-13CoarsenessInp-14(PSNR)Inp-15(SSIM) IndexInp-16(MSE)Inp-17(DC)Outp-1Target (0/1)In preprocessing layer, data normalization along with missing value handling is performed. Noisy data is dealt with the normalization technique. On the other hand, missing values are resolved using the mean and moving average of the existing values [35]. In the application training layer, two ML algorithms, ABPNN and SVM, are trained using preprocessed data.The output of ABPNN and SVM is given to the evaluation layer, where miss rate, accuracy, and Mean-Squared Error (MSE) are investigated. Then, an evaluation is done to find whether the Learning Criteria (LC) are met. If LC is met, it passes that data into the cloud. Otherwise, it must be retrained [36].The next step is to apply fuzzy logic to fuse the results of both techniques to improve the overall performance of the proposed technique. For testing purposes, the extracted attributes from CT scan images of the patient are fed to the fusion-based trained model that predicts whether the patient has a brain tumor or not. When LC is satisfied, the fusion-based trained model is stored on a central server [37].


### 3.1. ABPNN

ABPNN consists of the input, output, hidden layers, and the arrangement made from the back-propagation of error and feedforward propagation [38]. In forward propagation, data is composed of the input layer towards the hidden layer, eventually transferred to the output layer. The output layer is then directed in reverse to the procedure of back-propagation error if it is not accepted. Inconsistent weight figures are balanced to limit error and moved towards feedforward [39].Within the examination of the tumor, the input, output, and hidden layers are being utilized in ABPNN engineering with the feedforward algorithm using bit per data rate and conjunction [40]. In the current algorithm, distinct steps are associated. In the hidden layer, each neuron has an instigation work, e.g., f (x) = Sigmoid(x). Input capacity for the sigmoid function is presented in equation (1), and the sigmoid function in the hidden layer of the proposed system is composed as presented in equation(2).(1)netj=∑j=1aμij∗INPi+βi.(2)Outpj=21+e−netjwhere j=1,2,3…,n.The input parameter is taken from the output layer, as shown as follows:(3)€k=β2+∑i=1nδjk∗Outpj.The activation function of the output layer, as shown as follows:(4)Outpk=21+e−€kwhere1=1,2,3…,r.The per output neuron error is calculated with the help of the squared-error function and the sum of each of these to find the total error in (5)(5)ρ=12∑kεk−Outpk2.where the desired output is represented by εk and calculated output as Outpk. In (6), the output layer with the rate of weight change is written as(6)ΔW∝∂ρ∂w,Δδj,k=−∈∂ρ∂δj,k,(7)Δδj,k=−∈∂ρ∂Outpk∗∂Outpk∂€k∗∂€k∂δj,k,Δδj,k=∈εk−Outpk∗Outpk1−Outpk∗Outpj,(8)Δδj,k=∈ξkOutpj,ξk=εk−Outpk∗Outpk1−Outpk,Δμij∝−∑k∂ρ∂Outpk∗∂Outpk∂€k∗∂€k∂Outpj∗∂Outpj∂netj∗∂netj∂μij,Δμij=−∈∑k∂ρ∂Outpk∗∂Outpk∂€k∗∂€k∂Outpj∗∂Outpj∂netj∗∂netj∂μij,Δμij=−∈∑k∂ρ∂Outpk∗∂Outpk∂€k∗∂€k∂Outpj∗∂Outpj∂netj∗∂netj∂μij,Δμij=−∈∑kεk−Outpk∗Outpk1−Outpk∗δj,k∗Outpk1−Outpk∗INPi,Δμij=−∈∑kεk−Outpk∗Outpk1−Outpk∗δj,k∗Outpj1−Outpk∗INPi,Δμij=−∈∑kεk−Outpk∗Outpk1−Outpk∗δj,k∗Outpj1−Outpk∗INPi,ξj=−∈∑kξjδj,k∗Outpj1−Outpj∗INPi.The value of changed weight will be calculated by switching the values in (7) as intimated in (8), where, Outpk(9)Δμij=∈ξjINPi,where(10)ξj=∑kξjδj,k∗Outpj1−Outpj.The hidden and output layers are shown in (11), updating the bias and weight between them.(11)δj,kt+1=δj,kt++λΔδj,k.The updating values of bias and weight among the input layer and the hidden layer are exhibited as follows:(12)μijt+1=μijt++λΔμij.The learning rate of the brain tumor system model is represented by “λ.”


### 3.2. SVM

SVM is defined as a supervised ML algorithm that can either be used for regression or classification. Though, it is more commonly used in classification problems. Each data item is plotted in N-dimensional space (N represents total features) per feature’s amount of a specific coordinate in the SVM algorithm [41, 42].As the line equation is(13)χ2=aχ1+b,where “a” is the line slope and “b” is the intercept of the line.(14)aχ1−χ2+b=0.Let supposex¯=χ1,χ2T & ω¯=a−1. Now the beyond equation could be narrated as(15)ω.⟶x¯+b=0.The following equation is the resultant of 2-dimensional vectors. Equation (13) is also referred to as a hyperlane equation. The vector’s direction x¯=χ1,χ2 is symbolized as ω¯.(16)ω=x1x+x2x,where(17)x=xi2+x22+x32+⋯+xn2.As we discern,(18)cosℶ=x1x,cosρ=x2x.Equation (16) can be inscribed as(19)ω=cosℶ,cosρω⟶⋅x⟶=ωxcosℶ.Asℶ=ϑ−ρ, then(20)cosℶ=cosϑ−cosρcosℶ=cosϑcosρ−sinϑsinρ.cosℶ can also be written as(21)cosℶ=ω1ωx1x+ω2ωx2x.By simplifying the above equation(22)cosℶ=ω1x1+ω2x2ωx.Put the value ofcosℶ is (19)(23)ω⟶⋅x⟶=ωxω1x1+ω2x2ωx.As the above equation explains the 2-dimensional vectors, for then-dimensional vector, it can be written as shown in the following equation:(24)ω⟶⋅x⟶=∑i=1nωixiwhere i=1,2,…,n.The above equation is used to validate the correctly classifying the data(25)D=y¨w.x+b.“d” is called the functional margin of the dataset and is written as(26)d=mini=1…mDi.The hyperplane is selected as favorable, which has the largest value, whered is called the geometric margin of the dataset and we find out the optimal hyperplane in this article. To find out the optimal hyperplane, use the Lagrangian function, i.e., [43].(27)γω,b,ρ=12ω⋅ω−∑i=1mρiy:ω.x+b−1,∇ωγω,b,ρ=ω−∑i=1mρiyixi=0.(28)∇bγω,b,ρ=−∑i=1mρiyi=0.Obtaining from (27) and (28), we can write equation (18).(29)ω=∑i=1mρiyixiand∑i=1mρiyi=0.By substituting the Lagrangian function Ɣ(30)ωρ,b=∑i=1mρi−12∑i=1m.∑j=1mρiρjyiyjxixj.Thus, the above equation can also be defined in equation (19).(31)maxϐ∑i=1mρi−12∑i=1m.∑j=1mρiρjyiyjxixj.where i = 1, 2, 3, … , m.Because of inequalities in constraints, the “L” multiplier method is spread to the Karush–Kuhn–Tucker (KKT) conditions. KKT complementary condition states that(32)ρiyiωi⋅x∗+b−1=0.In the above equation,x∗ is the optimal point and ϐ is the positive value, and for other points, its values are nearly equal to zero. So, we can write as in equation (20)(33)yiωi⋅x∗+b−1=0.These are the closest points to the hyperplane, also known as support vectors. According to (33),(34)ω−∑i=1mρiyixi=0.It can also be written as(35)ω=∑i=1mρiyixi.Equation (35) gets when we compute the value of b(36)yiωi⋅x∗+b−1=0.Multiply both sides withyi(37)yi2ωi⋅x∗+b−1=0.As we knowy2/i. is equal to 1(38)b=yi−ωi⋅x∗,(39)b=1S∑i=1Syi−ω.x.In equation (39), S is the number of support vectors, and on the hyperplane, we make the predictions.The hypothesis function is described in (40)(40)USVM=Ήωi=+1ifω.x+b≥0,−1ifω.x+b<0.Class +1 will be categorized as an above point in the hyperplane, whereas −1 will be below the hyperplane (congestion not found). So, fundamentally, the main objective of the SVM algorithm is to calculate a hyperplane. It will distinguish the data correctly, and an optimal hyperplane is considered the best [1].


### 3.3. Decision-Based Fusion Empowered by Fuzzy Logic (DBFEFL)

Fusion of data and information can be considered into three levels of abstraction: feature fusion, classifier fusion (also classified as decision-based fusion), and data fusion [44]. Decision fusion is considered a form of data fusion that combines the decisions of multiple classifiers into a mutual decision. It furthermore provides the benefit of recompensing for the insufficiencies of the specific sensor by using one or more than one added sensor [45].The proposed DBFEFL is all about capability, intelligence, and logic. Fuzzy logic tries to handle problems with an imprecise and open set of data, sorting its chances of getting a flawless result [46]. The proposed DBFEFL for brain tumor diagnosis can be mathematically written as(41)μABPNN∩​μSVMABPNN,SVM=minμABPNNABPNN,μSVMSVMAccording to output parameters, ABPNN’s possible outcomes can be 0 or 1. Similarly, SVM’s possible outcomes can either be 0 or 1. So, according to fuzzy logic, we have four fuzzy rules.R1  = If ABPNN outcome is 1 and SVM outcome is 1, a brain tumor is detected.R2  = If ABPNN outcome is 0 and SVM outcome is 0, brain tumor is not detected.R3  = If ABPNN outcome is 1 and SVM outcome is 0, a brain tumor is detected.R4  = If ABPNN outcome is 0 and SVM outcome is 1, a brain tumor is detected.These rules are shown in the lookup diagram in Figure4.Figure 4
Fuzzy rules lookup diagram.Figure5 describes the surface viewer of the rules, that if ABPNN and SVM are from 0 to 40, the fuzzy decision is 0, which means a brain tumor is not detected. When the value is increased from 40 to 60, fuzzy is between 0-1, which means it can be a tumor. But when the value is greater than 60, the fuzzy decision is 1, which means a brain tumor is detected [47].Figure 5
Fuzzy rules surface viewer.Membership function:(42)Detection=DμDdμD,Nod=60−d2010≤d≤40,40≤d≤60,040≤d,Detection=DμDdμD,yesd=d−40200d≤40,40≤d≤60,160≤d≤100.


## 3.1. ABPNN

ABPNN consists of the input, output, hidden layers, and the arrangement made from the back-propagation of error and feedforward propagation [38]. In forward propagation, data is composed of the input layer towards the hidden layer, eventually transferred to the output layer. The output layer is then directed in reverse to the procedure of back-propagation error if it is not accepted. Inconsistent weight figures are balanced to limit error and moved towards feedforward [39].Within the examination of the tumor, the input, output, and hidden layers are being utilized in ABPNN engineering with the feedforward algorithm using bit per data rate and conjunction [40]. In the current algorithm, distinct steps are associated. In the hidden layer, each neuron has an instigation work, e.g., f (x) = Sigmoid(x). Input capacity for the sigmoid function is presented in equation (1), and the sigmoid function in the hidden layer of the proposed system is composed as presented in equation(2).(1)netj=∑j=1aμij∗INPi+βi.(2)Outpj=21+e−netjwhere j=1,2,3…,n.The input parameter is taken from the output layer, as shown as follows:(3)€k=β2+∑i=1nδjk∗Outpj.The activation function of the output layer, as shown as follows:(4)Outpk=21+e−€kwhere1=1,2,3…,r.The per output neuron error is calculated with the help of the squared-error function and the sum of each of these to find the total error in (5)(5)ρ=12∑kεk−Outpk2.where the desired output is represented by εk and calculated output as Outpk. In (6), the output layer with the rate of weight change is written as(6)ΔW∝∂ρ∂w,Δδj,k=−∈∂ρ∂δj,k,(7)Δδj,k=−∈∂ρ∂Outpk∗∂Outpk∂€k∗∂€k∂δj,k,Δδj,k=∈εk−Outpk∗Outpk1−Outpk∗Outpj,(8)Δδj,k=∈ξkOutpj,ξk=εk−Outpk∗Outpk1−Outpk,Δμij∝−∑k∂ρ∂Outpk∗∂Outpk∂€k∗∂€k∂Outpj∗∂Outpj∂netj∗∂netj∂μij,Δμij=−∈∑k∂ρ∂Outpk∗∂Outpk∂€k∗∂€k∂Outpj∗∂Outpj∂netj∗∂netj∂μij,Δμij=−∈∑k∂ρ∂Outpk∗∂Outpk∂€k∗∂€k∂Outpj∗∂Outpj∂netj∗∂netj∂μij,Δμij=−∈∑kεk−Outpk∗Outpk1−Outpk∗δj,k∗Outpk1−Outpk∗INPi,Δμij=−∈∑kεk−Outpk∗Outpk1−Outpk∗δj,k∗Outpj1−Outpk∗INPi,Δμij=−∈∑kεk−Outpk∗Outpk1−Outpk∗δj,k∗Outpj1−Outpk∗INPi,ξj=−∈∑kξjδj,k∗Outpj1−Outpj∗INPi.The value of changed weight will be calculated by switching the values in (7) as intimated in (8), where, Outpk(9)Δμij=∈ξjINPi,where(10)ξj=∑kξjδj,k∗Outpj1−Outpj.The hidden and output layers are shown in (11), updating the bias and weight between them.(11)δj,kt+1=δj,kt++λΔδj,k.The updating values of bias and weight among the input layer and the hidden layer are exhibited as follows:(12)μijt+1=μijt++λΔμij.The learning rate of the brain tumor system model is represented by “λ.”


## 3.2. SVM

SVM is defined as a supervised ML algorithm that can either be used for regression or classification. Though, it is more commonly used in classification problems. Each data item is plotted in N-dimensional space (N represents total features) per feature’s amount of a specific coordinate in the SVM algorithm [41, 42].As the line equation is(13)χ2=aχ1+b,where “a” is the line slope and “b” is the intercept of the line.(14)aχ1−χ2+b=0.Let supposex¯=χ1,χ2T & ω¯=a−1. Now the beyond equation could be narrated as(15)ω.⟶x¯+b=0.The following equation is the resultant of 2-dimensional vectors. Equation (13) is also referred to as a hyperlane equation. The vector’s direction x¯=χ1,χ2 is symbolized as ω¯.(16)ω=x1x+x2x,where(17)x=xi2+x22+x32+⋯+xn2.As we discern,(18)cosℶ=x1x,cosρ=x2x.Equation (16) can be inscribed as(19)ω=cosℶ,cosρω⟶⋅x⟶=ωxcosℶ.Asℶ=ϑ−ρ, then(20)cosℶ=cosϑ−cosρcosℶ=cosϑcosρ−sinϑsinρ.cosℶ can also be written as(21)cosℶ=ω1ωx1x+ω2ωx2x.By simplifying the above equation(22)cosℶ=ω1x1+ω2x2ωx.Put the value ofcosℶ is (19)(23)ω⟶⋅x⟶=ωxω1x1+ω2x2ωx.As the above equation explains the 2-dimensional vectors, for then-dimensional vector, it can be written as shown in the following equation:(24)ω⟶⋅x⟶=∑i=1nωixiwhere i=1,2,…,n.The above equation is used to validate the correctly classifying the data(25)D=y¨w.x+b.“d” is called the functional margin of the dataset and is written as(26)d=mini=1…mDi.The hyperplane is selected as favorable, which has the largest value, whered is called the geometric margin of the dataset and we find out the optimal hyperplane in this article. To find out the optimal hyperplane, use the Lagrangian function, i.e., [43].(27)γω,b,ρ=12ω⋅ω−∑i=1mρiy:ω.x+b−1,∇ωγω,b,ρ=ω−∑i=1mρiyixi=0.(28)∇bγω,b,ρ=−∑i=1mρiyi=0.Obtaining from (27) and (28), we can write equation (18).(29)ω=∑i=1mρiyixiand∑i=1mρiyi=0.By substituting the Lagrangian function Ɣ(30)ωρ,b=∑i=1mρi−12∑i=1m.∑j=1mρiρjyiyjxixj.Thus, the above equation can also be defined in equation (19).(31)maxϐ∑i=1mρi−12∑i=1m.∑j=1mρiρjyiyjxixj.where i = 1, 2, 3, … , m.Because of inequalities in constraints, the “L” multiplier method is spread to the Karush–Kuhn–Tucker (KKT) conditions. KKT complementary condition states that(32)ρiyiωi⋅x∗+b−1=0.In the above equation,x∗ is the optimal point and ϐ is the positive value, and for other points, its values are nearly equal to zero. So, we can write as in equation (20)(33)yiωi⋅x∗+b−1=0.These are the closest points to the hyperplane, also known as support vectors. According to (33),(34)ω−∑i=1mρiyixi=0.It can also be written as(35)ω=∑i=1mρiyixi.Equation (35) gets when we compute the value of b(36)yiωi⋅x∗+b−1=0.Multiply both sides withyi(37)yi2ωi⋅x∗+b−1=0.As we knowy2/i. is equal to 1(38)b=yi−ωi⋅x∗,(39)b=1S∑i=1Syi−ω.x.In equation (39), S is the number of support vectors, and on the hyperplane, we make the predictions.The hypothesis function is described in (40)(40)USVM=Ήωi=+1ifω.x+b≥0,−1ifω.x+b<0.Class +1 will be categorized as an above point in the hyperplane, whereas −1 will be below the hyperplane (congestion not found). So, fundamentally, the main objective of the SVM algorithm is to calculate a hyperplane. It will distinguish the data correctly, and an optimal hyperplane is considered the best [1].


## 3.3. Decision-Based Fusion Empowered by Fuzzy Logic (DBFEFL)

Fusion of data and information can be considered into three levels of abstraction: feature fusion, classifier fusion (also classified as decision-based fusion), and data fusion [44]. Decision fusion is considered a form of data fusion that combines the decisions of multiple classifiers into a mutual decision. It furthermore provides the benefit of recompensing for the insufficiencies of the specific sensor by using one or more than one added sensor [45].The proposed DBFEFL is all about capability, intelligence, and logic. Fuzzy logic tries to handle problems with an imprecise and open set of data, sorting its chances of getting a flawless result [46]. The proposed DBFEFL for brain tumor diagnosis can be mathematically written as(41)μABPNN∩​μSVMABPNN,SVM=minμABPNNABPNN,μSVMSVMAccording to output parameters, ABPNN’s possible outcomes can be 0 or 1. Similarly, SVM’s possible outcomes can either be 0 or 1. So, according to fuzzy logic, we have four fuzzy rules.R1  = If ABPNN outcome is 1 and SVM outcome is 1, a brain tumor is detected.R2  = If ABPNN outcome is 0 and SVM outcome is 0, brain tumor is not detected.R3  = If ABPNN outcome is 1 and SVM outcome is 0, a brain tumor is detected.R4  = If ABPNN outcome is 0 and SVM outcome is 1, a brain tumor is detected.These rules are shown in the lookup diagram in Figure4.Figure 4
Fuzzy rules lookup diagram.Figure5 describes the surface viewer of the rules, that if ABPNN and SVM are from 0 to 40, the fuzzy decision is 0, which means a brain tumor is not detected. When the value is increased from 40 to 60, fuzzy is between 0-1, which means it can be a tumor. But when the value is greater than 60, the fuzzy decision is 1, which means a brain tumor is detected [47].Figure 5
Fuzzy rules surface viewer.Membership function:(42)Detection=DμDdμD,Nod=60−d2010≤d≤40,40≤d≤60,040≤d,Detection=DμDdμD,yesd=d−40200d≤40,40≤d≤60,160≤d≤100.


## 4. Experimental Analysis

The proposed system is developed using MATLAB 2017. For experimental analysis, the dataset is divided into training and testing phases. 2634 samples are used for training, which is 70% of the data sample. 1128 samples are used for testing, i.e., 30% of the data samples [47, 48]. To evaluate the proposed system, several performance measure metrics are used that are computed with the help of equations (27) to (36) [49].(43)Miss rate=O1/T0+O0/T1T0+T1,(44)Accuracy=O0/T0+O1/T1T0+T1,(45)Positive prediction value=O10/T1O0/T1+O1/T1,(46)Negative prediction value=O0/T0O0/T1+O1/T1,(47)Specifcity=O0/T0O0/T0+O0/T1,(48)Sensitivity=O1/T1O1/T0+O1/T1,(49)False_positive_ratio=1−specificity,(50)False_positive_ratio=1−Sensitivity,(51)Likelihood_ratio_positive=Sensitivity1−specicity,(52)Likelihood_ratio_negative=1−Sensitivityspecifcity.The input parameters for the ABPNN and SVM algorithms are listed in Tables3 and 4, respectively [50–52]. Tables 5 and 6 show the confusion matrix of ABPNN during the training and testing phase, respectively.Table 3
Input parameters for ABPNN.
Hyper-parametersValueAlgorithmScaled conjugate gradientHidden layers22Epochs11Momentum32Cross-validation5Table 4
Input parameters for SVM.
Hyper-parametersValueCross validation5PenaltyL0, L1LossHingeKernelLinearTable 5
Confusion matrix of ABPNN (training phase).
N = 2634 (no. of samples)Result (output)O0,O1InputExpected output (T0,T1)O0 (0)O1 (1)T0=1682 (0)167210T1=952 (1)25927Table 6
Confusion matrix of ABPNN (testing phase).
N = 1128 (no. of samples)Result (output)O0,O1InputExpected output (T0,T1)O0 (0)O1 (1)T0=397 (0)3934T1=731 (1)33698Tables7 and 8 show the confusion matrix of SVM during the training and testing phase, respectively. Tables 9 and 10 show the confusion matrix of DBFEFL during the training and testing phase, respectively.Table 7
Confusion matrix of SVM (training phase).
N = 2634 (no of samples)Result (output)O0,O1InputExpected output (T0,T1)O0 (0)O1 (1)T0=1682 (0)16757T1=952 (1)33919Table 8
Confusion matrix of SVM (testing phase).
N = 1128 (no of samples)Result (output)O0,O1InputExpected output (T0,T1)O0 (0)O1 (1)T0=397 (0)3898T1=731 (1)18713Table 9
Confusion matrix of DBFEFL (training phase).
N = 2634 (no of samples)Result (output)O0,O1InputExpected output (T0,T1)O0 (0)O1 (1)T0=1682 (0)16757T1=952 (1)25927Table 10
Confusion matrix of DBFEFL (testing phase).
N = 1128 (no of samples)Result (output)O0,O1InputExpected output (T0,T1)O0 (0)O1 (1)T0=397 (0)3907T1=731 (1)19712Table11 lists the experimental results of the proposed brain tumor detection system at each stage in terms of several performance evaluation metrics [53]. During the testing phase, there is a 97.81% accuracy and a 2.19% miss rate. For the ABPNN model, the accuracy is 98.67% and the miss rate is 1.33% in the training phase. The accuracy and miss rates are 96.72% and 3.28% in the testing phase, respectively. In the SVM model, attained accuracy is 98.48% and the miss rate is 1.52% in the training phase. On the other hand, 97.70% accuracy and 2.3% miss rate are achieved in the testing phase. It can be seen that DBFEFL has an accuracy of 98.79% and a miss rate of 1.21% in the training phase.Table 11
Experimental results of the proposed system.
MeasuresABPNN (training)ABPNN (testing)SVM (training)SVM (testing)DBFEFL (training)DBFEFL (testing)Accuracy98.67%96.72%98.48%97.70%98.79%97.81%Miss rate1.33%3.28%1.52%2.3%1.21%2.19%Sensitivity98.93%99.43%99.24%98.89%99.25%99.03%Specificity98.53%92.25%98.07%95.52%98.53%95.35%Precision97.37%95.49%96.54%97.54%97.37%97.4%Negative predictive value99.41%98.99%99.58%97.89%99.58%98.24%False positive rate1.477.751.934.421.474.65False negative rate1.070.570.761.110.750.97Table12 shows a comparative analysis of the proposed system with existing methods using the same dataset taken from the Kaggle website [7]. The experimental results revealed that the proposed method DBFEFL has achieved the highest accuracy with better performance using the latest dataset with the maximum number of samples. The accuracy of the proposed method DBFEFL is 97.81% with the latest dataset of 3762 samples. Whereas the maximum accuracy attained using the Cross-Validated NGBoost Classifier [25] is 98.54%, they use 1644 images. Similarly, the maximum accuracy attained by using the Cross-Validated AdaBoost Classifier [26] is 98.97%, but similarly, they are using 1644 images. The accuracy using BPNN [28] is 87.01% using the same number of samples.Table 12
Comparative analysis between the proposed and existing methods.
AuthorTechniqueBRATS datasetProposedDBFEFL (97.81%)3672 imagesDutta & Bandyopadhyay [25]Cross-validated NGBoost classifier (98.54%)1644 imagesGradient boost (97.37%)AdaBoost (98.18%)Random forest (97.98%)Extra trees (94.13%)Dutta & Bandyopadhyay [26]Cross-validated AdaBoost classifier (98.97%)1644 imagesGradient boost (90.69%)Random forest (98.18%)Extra trees (94.33%)Munajat & Utaminingrum [28]BPNN (87.01%)3762 images


## 5. Conclusion

Early detection of brain tumors helps to decrease the casualty rate of brain tumor patients. The brain tumor manual diagnostic procedure is done with the help of domain specialists, which is an extraordinary time taking task. To automate this process, this paper presented a system for brain tumor detection that exploited ABPNN, SVM, and fuzzy logic to achieve the desired results. The outcomes of ABPNN and SVM are fused using fuzzy logic to increase the system’s overall accuracy. The experimental results showed an accuracy of 98.30% and a miss rate of 1.7%. This research will be helpful in the medical science field. It can be deployed in OPD for brain tumor detection. It can be transformed into an interactive app that will take CT-scan images as an input parameter and categorize the patient as infected or normal. It may be helpful for doctors as an assistant hand for them that may strengthen their opinion regarding the diagnosis of the brain tumor patient.



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