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Application of Fuzzy Logic in the Ranking of Academic Institutions

Application of Fuzzy Logic in the Ranking of Academic Institutions FUZZY INFORMATION AND ENGINEERING 2019, VOL. 11, NO. 3, 295–306 https://doi.org/10.1080/16168658.2020.1805253 Application of Fuzzy Logic in the Ranking of Academic Institutions a b c d e Kousik Das , Sovan Samanta , Usman Naseem , Shah Khalid Khan and Kajal De a b Department of Mathematics, D. J. H. School, Dantan, India; Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, India; School of Computer Science, University of Technology Sydney, Sydney, d e Australia; School of Engineering, RMIT University, Carlton, Australia; Department of Mathematics, Netaji Subhas Open University, Kolkata, India ABSTRACT ARTICLE HISTORY Received 11 October 2019 For the development of any organization, evaluation of performance Revised 14 July 2020 is an important task. To analyze the performance, Das et al. intro- Accepted 17 July 2020 duced a ranking framework based on fuzzy logic. That framework compared the current NIRF system of Indian Institutions with the KEYWORDS fuzzy logic-based Mamdani system, KSM index. In that study, uniform Fuzzy control system; NIRF; membership functions are not taken. This study will focus on the KSM index; Sugeno ranking system based on Mamdani and Sugeno with fuzzy triangular numbers as input values of membership functions. Also, the updated results are compared with existing NIRF systems and considered Top 20 institutions of India for the year 2019 as per NIRF. 1. Introduction Education is a basic need for our society and life. The government of India provides qual- ity education to the people for free and compulsory [1] at the primary level. Many higher education institutions in India provide quality education and develop our society. Like eval- uation of students every year, every institution needs to analyze their performances. To compare the performances among institutions, there must need a ranking framework. A most well-known method for ranking higher institutions by MHRD (Govt. of India) is the National Institutional Ranking Framework (NIRF) [2]. Generally, the ranking of Indian institutes is done by NIRF, Govt of India based on crisp weighted data. But, these crisp data sometimes are less significant when grading systems are used. Fuzzy logic is better to represent such linguistic variables as low, medium, or high. Fuzzy logic handles the imprecise and vagueness data. Fuzzy logic, algorithm, and decision making first introduced by L. A. Zadeh [3–6]. After that, E. H. Mamdani [7,8] applied fuzzy logic to control an automatic stream engine. Fuzzy logic [9,10] has been applied in many areas like decision making [11,12] automatic control, banks, hospitals, and academic insti- tutions [13–16]. Moon et al. proposed a model for performance analysis and promotion ranking [17] in military organizations in Korea In [18], Srinivasan et al., introduced percep- tion based performance analysis of higher institutions. In that paper, authors considered CONTACT Sovan Samanta ssamantavu@gmail.com © 2021 The Author(s). Published by Taylor & Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society of China & Operations Research Society of Guangdong Province. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. 296 K. DAS ET AL. students, faculty, research investor, and public as perceptions, and this model is based on various parameters also, but did not survey any real data. In [19], Das et al. introduced the KSM index of ranking educational institutions based on fuzzy systems. In that study, input membership values are assumed as per the weight of the input data as per Mamdani rule-based systems. The crisp result is obtained through the defuzzification of rules’ in the Mamdani system. Combining more than two inputs in crisp data needs lots of rules. For example, if you say teaching got 90% credit, Research got 70%, and Infrastructure got 50% credits. These rules will give an output. At the same time, changing a bit like teaching got 89% credit, Research got 72%, and Infrastructure got 51% credits, the rule will be changed. So infinite numbers of rules are to be prepared. Fuzzy logic is adapted realistically. Rules are limited as the parameters are divided into low, medium, high category or few more. Few more survey can be found in [20–26]. In the current NIRF system, few drawbacks are seen. Crisp weighted results are assumed for ranking. As per data collection, the input values are crisp. But to evaluate teaching- learning, Infrastructure, and research publications, fuzzy credentials are much realistic. Thus, instead of crisp inputs, fuzzy inputs are rather helpful and justified. This problem has been addressed by KSM Index in the paper by Das et al.. In KSM Index, the major drawback is that the inputs are used without uniformity. In our proposed study, the techniques of the KSM Index have been advanced. Besides, the ranking is provided based on Sugeno fuzzy rule-based systems. And finally, a comparison is made with Mamdani, Sugeno, and crisp NIRF methods. To study this, we collected data of the top 20 higher institutes of India as per NIRF 2019 and illustrated the results. The rest of the paper is organized as follows. In section 2, we studied some basic concepts on fuzzy logic and rule base system and NIRF system. In section 3, we proposed our model and discussed and comparing the result with the existing model. In section 4, we conclude the model with future directions. 2. Preliminaries In this section, we studied the basic knowledge of fuzzy logic, fuzzy inference system and existing NIRF system. 2.1. Fuzzy Logic An extension of the classical set is a fuzzy set where each object of the fuzzy set have some degree of membership between the values 0 and 1. Let X be non-empty set, then a fuzzy set Z in X is defined as Z ={x, µ (x) : x ∈ X} where µ (x) is the membership function of x in Z and the value of µ (x) lies between 0 and z z 1insuchawaythat ⎪ 1, x is strongly lies in X µ (x) = z (0, 1), x is partially lies in x 0, x is not in X. FUZZY INFORMATION AND ENGINEERING 297 Figure 1. Membership function of temperature. A mapping from any input set to a degree of membership between 0 and 1 is called a membership function. A triangular membership function is defined as x − a if a ≤ x < b ⎪ b − a 1 if x = b µ (x) = c − x if b ≤ x < c ⎪ c − b 0 otherwise In traditional logic, an element in the set completely belongs to the set or not that is 0 or 1. In the real world, we lead with ambiguities, vague concepts that are smoothly handled by fuzzy logic. It has applications in many fields like automation technology, control, robotics, image processing, medical diagnosis, pattern recognition, etc. To save energy, many fuzzy logic-based home appliances like refrigerators are being invented. Fuzzy logic is associated with an important term linguistic variable. It represents a word like ‘temperature’, ‘age’, etc. where the temperature may be very cool, cool, hot, very hot. So these are actually fuzzy membership functions (Figure 1). For further studies, readers can check the references [27–29]. 2.2. Fuzzy Inference System Fuzzy inference system (FIS) is a complete process that works on a given set of crisp inputs to crisp output based on fuzzy logic. It has four parts that are fuzzification, fuzzy rule base, fuzzy inference, and defuzzification. In fuzzification, all crisp inputs convert into fuzzy linguistic value. Then if-else rules are defined on these linguistic values. After that, all combinations of fuzzy rules with membership functions are performed to produce fuzzy output using AND, OR, NOT, etc. operations. In defuzzification, all fuzzy outputs convert into crisp value by any method (Centroid, MOM, etc.). A diagram for FIS is shown in Figure 2. 298 K. DAS ET AL. Figure 2. FIS system. Table 1. NIRF parameters. Sl. No. Parameters Marks Weightage 1 Teaching, Learning & Resources (TLR) 100 0.30 2 Research and Professional Practice (RPP) 100 0.30 3 Graduation Outcomes (GO) 100 0.20 4 Outreach and Inclusivity (OI) 100 0.10 5 Perception (PR) 100 0.10 2.3. NIRF System To evaluate the performance of the higher institutions in India and ranking the insti- tutions, MHRD approved a system in 2015 called NIRF (National Institutional Ranking Framework). This system of evaluation consists of five major parameters. These are “Teach- ing, Learning and Resources(TLR),’ ‘Research and Professional Practices(RPP),’ ‘Graduation Outcomes(GO),’ ‘Outreach and Inclusivity(OI),’ and ‘Perception(PR)’. The weightage value considers in this system for these parameters are given in the table. NIRF calculates the score of an institution by a weighted sum method. All parameters are summarized following in the table (Table 1). 3. Method for Evaluation of Performance In practical, all input parameters (TLR, RPP, GO, OI, PR) are linguistic terms. So all parameters have linguistic values with some degree of memberships. We design a fuzzy logic rule base system considering these parameters to get the new score. The index has the following brief steps. Algorithm: Input: Percentage of TLR, RPP, GO and PR for each institute. Output: Score of a ranking framework based on a fuzzy logic system. Step- I: Construct all membership functions for all input parameters ‘TLR’, ‘RPP’, ‘GO’, ‘OI’, ‘PR’ as triangular fuzzy numbers and the same for output parameter ‘score’ in Mam- dani/Sugeno FIS. Step-II: Define fuzzy rule base on these parameters. This rule-base follows the rules of NIRF as per the weights. That is the weight ratio for the input parameters are 3:3:2:1:1. FUZZY INFORMATION AND ENGINEERING 299 Figure 3. Membership function for input and output parameter. Table 2. Ranges of input and output parameters. Input/Output Parameter Linguistic values Range TLR, RPP, GO, OI, PR, Score Low (1) (−40, 0, 40) Medium (2) (10, 50, 90) High (3) (60, 100, 140) Step-III: Use Mamdani/Sugeno computation tool for combining membership functions with the fuzzy rules to derive the fuzzy output and finally crisp output. 3.1. Membership Functions The details range of linguistic input parameters and an output parameter (Table 2)aretaken uniformly, and the corresponding membership function (Figure 3) is given below. 3.2. Fuzzy Rule Base In our study, we considered five inputs and one output. Combining all these inputs, we developed all possible 243 IF-THEN rules. All the rules are shown below in Table 3. 3.3. Results and Observations A comparision of inputs (TLR, RP, GO, OI and PR) of academic institutions are shown in Figure 4. We got the score of all institutions as per given inputs (Table 4) using two tools Mamdani and Sugeno. An input and output score of DU is shown in Figure 5.Asurface viewer is shown in Figure 6. The results are compared with the existing model in Table 4. Comparing ranking in all methods for the institutions are shown in Table 5.Agraphical comparison between NIRF and fuzzy logic-based model is shown in Figure 7. We observed from that the results that i. Scores of the assumed institutes based on Sugeno are higher than that of Mamdani. ii. The rank of the top twenty institutes of India according to NIRF method and other two fuzzy logic methods are shown in Table 5. All three methods suggest that IITM and IISC 300 K. DAS ET AL. Table 3. If-Then rule base. Sr. No TLR RP GO OI PR Output Sr. No TLR RP GO OI PR Output 1 1 11 1 1 1 31 1 21 2 1 1 2 1 11 1 2 1 32 1 21 2 2 2 3 1 11 1 3 1 33 1 21 2 3 2 4 1 11 2 1 1 34 1 21 3 1 2 5 1 11 2 2 1 35 1 21 3 2 2 6 1 11 2 3 1 36 1 21 3 3 2 7 1 11 3 1 1 37 1 22 1 1 1 8 1 11 3 2 2 38 1 22 1 2 2 9 1 11 3 3 2 39 1 22 1 3 2 10 1 1 2 1 1 1 40 1 2 2 2 1 2 11 1 1 2 1 2 1 41 1 2 2 2 2 2 12 1 1 2 1 3 1 42 1 2 2 2 3 2 13 1 1 2 2 1 1 43 1 2 2 3 1 2 14 1 1 2 2 2 1 44 1 2 2 3 2 2 15 1 1 2 2 3 2 45 1 2 2 3 3 2 16 1 1 2 3 1 2 46 1 2 3 1 1 2 17 1 1 2 3 2 2 47 1 2 3 1 2 2 18 1 1 2 3 3 2 48 1 2 3 1 3 2 19 1 1 3 1 1 1 49 1 2 3 2 1 2 20 1 1 3 1 2 2 50 1 2 3 2 2 2 21 1 1 3 1 3 2 51 1 2 3 2 3 2 22 1 1 3 2 1 2 52 1 2 3 3 1 2 23 1 1 3 2 2 2 53 1 2 3 3 2 2 24 1 1 3 2 3 2 54 1 2 3 3 3 3 25 1 1 3 3 1 2 55 1 3 1 1 1 1 26 1 1 3 3 2 2 56 1 3 1 1 2 2 27 1 1 3 3 3 2 57 1 3 1 1 3 2 28 1 2 1 1 1 1 58 1 3 1 2 1 2 29 1 2 1 1 2 1 59 1 3 1 2 2 2 30 1 2 1 1 3 1 60 1 3 1 2 3 2 Sr. No TLR RP GO OI PR Output Sr. No TLR RP GO OI PR Output 61 1 3 1 3 1 2 92 2 1 2 1 2 1 62 1 3 1 3 2 2 93 2 1 2 1 3 2 63 1 3 1 3 3 2 94 2 1 2 2 1 2 64 1 3 2 1 1 2 95 2 1 2 2 2 2 65 1 3 2 1 2 2 96 2 1 2 2 3 2 66 1 3 2 1 3 2 97 2 1 2 3 1 2 67 1 3 2 2 1 2 98 2 1 2 3 2 2 68 1 3 2 2 2 2 99 2 1 2 3 3 2 69 1 3 2 2 3 2 100 2 1 3 1 1 2 70 1 3 2 3 1 2 101 2 1 3 1 2 2 71 1 3 2 3 2 2 102 2 1 3 1 3 2 72 1 3 2 3 3 3 103 2 1 3 2 1 2 73 1 3 3 1 1 2 104 2 1 3 2 2 2 74 1 3 3 1 2 2 105 2 1 3 2 3 2 75 1 3 3 1 3 2 106 2 1 3 3 1 2 76 1 3 3 2 1 2 107 2 1 3 3 2 2 77 1 3 3 2 2 3 108 2 1 3 3 3 3 78 1 3 3 2 3 3 109 2 2 1 1 1 1 79 1 3 3 3 1 2 110 2 2 1 1 2 2 80 1 3 3 3 2 3 111 2 2 1 1 3 2 81 1 3 3 3 3 3 112 2 2 1 2 1 2 82 2 1 1 1 1 1 113 2 2 1 2 2 2 83 2 1 1 1 2 1 114 2 2 1 2 3 2 84 2 1 1 1 3 2 115 2 2 1 3 1 2 85 2 1 1 2 1 2 116 2 2 1 3 2 2 86 2 1 1 2 2 2 117 2 2 1 3 3 2 87 2 1 1 2 3 2 118 2 2 2 1 1 2 88 2 1 1 3 1 2 119 2 2 2 1 2 2 89 2 1 1 3 2 2 120 2 2 2 1 3 2 (continued) FUZZY INFORMATION AND ENGINEERING 301 Table 3. Continued. Sr. No TLR RP GO OI PR Output Sr. No TLR RP GO OI PR Output 90 2 1 1 3 3 2 121 2 2 2 2 1 2 91 2 1 2 1 1 1 122 2 2 2 2 2 2 Sr. No TLR RP GO OI PR Output Sr. No TLR RP GO OI PR Output 123 2 2 2 2 3 2 154 2 3 3 1 1 2 124 2 2 2 3 1 2 155 2 3 3 1 2 2 125 2 2 2 3 2 2 156 2 3 3 1 3 2 126 2 2 2 3 3 3 157 2 3 3 2 1 2 127 2 2 3 1 1 2 158 2 3 3 2 2 2 128 2 2 3 1 2 2 159 2 3 3 2 3 3 129 2 2 3 1 3 2 160 2 3 3 3 1 2 130 2 2 3 2 1 2 161 2 3 3 3 2 3 131 2 2 3 2 2 2 162 2 3 3 3 3 3 132 2 2 3 2 3 2 163 3 1 1 1 1 1 133 2 2 3 3 1 2 164 3 1 1 1 2 2 134 2 2 3 3 2 3 165 3 1 1 1 3 2 135 2 2 3 3 3 3 166 3 1 1 2 1 2 136 2 3 1 1 1 1 167 3 1 1 2 2 2 137 2 3 1 1 2 2 168 3 1 1 2 3 2 138 2 3 1 1 3 2 169 3 1 1 3 1 2 139 2 3 1 2 1 2 170 3 1 1 3 2 2 140 2 3 1 2 2 2 171 3 1 1 3 3 2 141 2 3 1 2 3 2 172 3 1 2 1 1 2 142 2 3 1 3 1 2 173 3 1 2 1 2 2 143 2 3 1 3 2 2 174 3 1 2 1 3 2 144 2 3 1 3 3 2 175 3 1 2 2 1 2 145 2 3 2 1 1 2 176 3 1 2 2 2 2 146 2 3 2 1 2 2 177 3 1 2 2 3 2 147 2 3 2 1 3 2 178 3 1 2 3 1 2 148 2 3 2 2 1 2 179 3 1 2 3 2 2 149 2 3 2 2 2 2 180 3 1 2 3 3 3 150 2 3 2 2 3 2 181 3 1 3 1 1 2 151 2 3 2 3 1 2 182 3 1 3 1 2 2 152 2 3 2 3 2 2 183 3 1 3 1 3 2 153 2 3 2 3 3 3 184 3 1 3 2 1 2 Sr. No TLR RP GO OI PR Output Sr. No TLR RP GO OI PR Output 185 3 1 3 2 2 2 216 3 2 3 3 3 3 186 3 1 3 2 3 3 217 3 3 1 1 1 2 187 3 1 3 3 1 2 218 3 3 1 1 2 2 188 3 1 3 3 2 3 219 3 3 1 1 3 2 189 3 1 3 3 3 3 220 3 3 1 2 1 2 190 3 2 1 1 1 2 221 3 3 1 2 2 2 191 3 2 1 1 2 2 222 3 3 1 2 3 2 192 3 2 1 1 3 2 223 3 3 1 3 1 2 193 3 2 1 2 1 2 224 3 3 1 3 2 2 194 3 2 1 2 2 2 225 3 3 1 3 3 3 195 3 2 1 2 3 2 226 3 3 2 1 1 2 196 3 2 1 3 1 2 227 3 3 2 1 2 2 197 3 2 1 3 2 2 228 3 3 2 1 3 3 198 3 2 1 3 3 3 229 3 3 2 2 1 2 199 3 2 2 1 1 2 230 3 3 2 2 2 3 200 3 2 2 1 2 2 231 3 3 2 2 3 3 201 3 2 2 1 3 2 232 3 3 2 3 1 3 202 3 2 2 2 1 2 233 3 3 2 3 2 3 203 3 2 2 2 2 2 234 3 3 2 3 3 3 204 3 2 2 2 3 2 235 3 3 3 1 1 2 205 3 2 2 3 1 2 236 3 3 3 1 2 3 206 3 2 2 3 2 3 237 3 3 3 1 3 3 207 3 2 2 3 3 3 238 3 3 3 2 1 3 208 3 2 3 1 1 2 239 3 3 3 2 2 3 209 3 2 3 1 2 2 240 3 3 3 2 3 3 (continued) 302 K. DAS ET AL. Table 3. Continued. Sr. No TLR RP GO OI PR Output Sr. No TLR RP GO OI PR Output 210 3 2 3 1 3 3 241 3 3 3 3 1 3 211 3 2 3 2 1 2 242 3 3 3 3 2 3 212 3 2 3 2 2 3 243 3 3 3 3 3 3 213 3 2 3 2 3 3 214 3 2 3 3 1 3 215 3 2 3 3 2 3 Figure 4. Comparision of inputs. Figure 5. Score of DU. FUZZY INFORMATION AND ENGINEERING 303 Figure 6. Surface viewer. Figure 7. Graphical comparison among all models. are top two institutes in India. Again, the lowest spot among the top twenty is fixed to DU. iii. Figure 7 shows the comparative graphs of all three methods. Result of ranking based on NIRF and Mamdani is similar. The changes in the ranking are low, while the other method based on Sugeno has a significant difference. 304 K. DAS ET AL. Table 4. Input and output for all models. Sr. No. INSTITUTE TLR RP GO OI PR NIRF Sugeno Mamdani 1 IITM 84.57 83.54 87.13 66.08 94.14 83.88 97.2 71.7 2 IISC 83.16 89.24 78.56 50.69 86.92 82.28 94.4 67.4 3 IITD 78.3 82.98 79.13 58.58 86.14 78.69 86.2 62.9 4 IITB 76.95 84.37 82.32 50.69 86.92 78.62 88.7 65.2 5 IITKGP 67.35 76.65 86.17 60.63 78.11 74.31 82.7 60.5 6 IITK 71.96 69.61 69.96 50.39 75.68 69.07 62.6 55.6 7 JNU 76.75 41.85 99.87 75.87 55.27 68.68 89.6 60.2 8 IITR 67.32 65.08 87.14 61.64 43.66 67.68 63.2 53.1 9 IITG 76.8 56.58 73.87 60.63 46.34 65.47 63.5 57.9 10 BHU 69.72 46.48 96.37 57.02 47.28 64.55 66.2 54.5 11 HU 74.81 43.77 83.65 58.77 36.71 61.85 67.3 58.6 12 CU 62.26 47.1 91.54 60.14 37.39 60.87 53.6 50.7 13 JU 54.39 54.89 90.28 44.95 51.83 60.53 50 50 14 AU 56.39 54.09 78.07 53.16 62.72 60.35 52.7 50 15 AVV 73.02 43.77 70.28 70.23 31.01 59.22 61.7 55.5 16 MAHE 77.9 38.32 69.71 66.78 30.21 58.50 60.7 55.1 17 SPPU 69.25 44.42 86.04 54.33 16.55 58.40 52.9 53 18 AMU 76.69 35.38 85.66 57.57 18.46 58.36 55.7 54.6 19 JMI 73.75 32.04 88.53 71.97 14.26 58.07 59.2 56.7 20 DU 47.86 53.8 87.18 55.41 41.11 57.59 50 50 Table 5. Comparison of ranking for all models. Ranking NIRF(2019) Sugeno Mamdani 1 IITM IITM IITM 2 IISC IISC IISC 3 IITD JNU IITB 4 IITB IITB IITD 5 IITKGP IITD IITKGP 6 IITK IITKGP JNU 7 JNU HU HU 8 IITR BHU IITG 9 IITG IITG JMI 10 BHU IITR IITK 11 HU IITK AVV 12 CU AVV MAHE 13 JU MAHE AMU 14 AU JMI BHU 15 AVV AMU IITR 16 MAHE CU SPPU 17 SPPU SPPU CU 18 AMU AU JU 19 JMI JU AU 20 DU DU DU iv. Figure 7 also indicates that the ranking based on Mamdani and Sugeno is proportional. That means the peaks are at the same points. 4. Conclusion In the decision making and evaluation process, fuzzy logic has enormous applications. In this study, a fuzzy logic-based model for ranking higher institutions is proposed in both Mamdani and Sugeno tools. This study captures all real inputs and found a realistic result better from the crisp model. This study concludes that the results based on fuzzy logic are practical. In Sugeno, results are directly related to the crisp numbers, but in Mamdani, the FUZZY INFORMATION AND ENGINEERING 305 results are obtained due to defuzzification. Thus it is advisable to choose the consequences of Mamdani based system. The difference between the ranking is shown in Table 5 and Figure 7. Many companies and organizations are always finding the best evaluation tools for their performance analysis. In the future, the proposed model will be beneficial for all others rank- ing such as companies, publishers, countries, etc. to evaluate their performance. This type of ranking should apply to find the top institute to provide financial help, research grant, etc. to the sponsoring authority. Disclosure statement No potential conflict of interest was reported by the author(s). Notes on contributors Mr. Kousik Das has 3 years of research experience in graph theory, fuzzy graph theory and social net- works. He is working as a teacher at D.J.H. School, Dantan, West Bengal, India. He has published 10 articles and book chapters in Springer, IEEE Explore, IGI global, NSS, Hindawi publishers. Dr. Sovan Samanta is an Assistant Professor in the Department of Mathematics, Tamralipta Mahavidyalaya (Vidyasagar University). He worked as Assistant Professor in Indian Institute of Infor- mation Technology, Nagpur. He was a post-doc fellow at Hanyang University, Ansan, South Korea. He completed his Ph.D. from Vidyasagar University in Fuzzy Graph Theory. He introduced fuzzy planar graphs, fuzzy competition graphs, fuzzy tolerance graphs, etc. He published more than 60 articles in different reputed SCI/SCIE and Scopus Journals. His current research interests include data science, graph theory, social networks, and fuzzy graphs. Mr. Usman Naseem has received Master of Analytics (research) from Advanced Analytics Institute, University of Technology, Sydney, Australia in 2020. Currently, he is pursuing Ph.D in computer sci- ence. He has published several papers in well-reputed journals and conferences. His area of research includes social data analytics, natural language processing, health-care analytics and machine learn- ing. Mr. Shah Khalid Khan is a research scholar at RMIT University, Melbourne, Australia. He is a quali- fied ICT professional, having worked with multinational telecom vendors and operators in multiple domains for more than 08 years after doing B.E (Electrical Engineering) in 2008. He completed master by research degree from RMIT University, Melbourne, Australia. His research interests include next generation wireless networks, millimeter-wave technology, Connected and Autonomous Vehicles (CAVs), cybersecurity, data science, data analytics and machine learning techniques. Dr. Kajal De is a professor in the Department of Mathematics, Netaji Subhas Open University, India. Her research interest includes operations research, fuzzy algebra, fuzzy graphs etc. He has published many articles in various reputed journals. References [1] Right to education act, https://en.wikipedia.org/wiki/Right_of_Children_to_Free_and_Compu lsory_Education_Act_2009 [2] NATIONAL INSTITUTIONAL RANKING FRAMEWORK, Ministry of Human Resource Development, Government of India, www.nirf.org. [3] Zadeh LA. Fuzzy sets. Inf Control. 1965;8(3):338–353. [4] Zadeh LA. Fuzzy algorithms. Inf Control. 1968;94-102(12):94–102. [5] Zadeh LA. Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans Syst Man Cybern. 1973;3(1):28–44. 306 K. DAS ET AL. [6] Zadeh LA. Is there a need for fuzzy logic? Inf Sci (Ny). 2008;178:2751–2779. [7] Esragh F, Mamdani EH. A general approach to linguistic approximation. In: EH Mamdani, BR Gaines, editor. Fuzzy reasoning and its applications. London: Academic Press; 1981. https://dl.acm.org/doi/abs/10.5555/578304 [8] Mamdani EH, Assilion S. An experiment in linguistic synthesis with a fuzzy logic controller. Intl J Man-Mach Stud. 1975;7:1–13. [9] Zimmermann HJ. Fuzzy sets, decision making and expert systems. Boston: Kluwer; 1987. [10] Srivastav MK, Bhadoria RS, Pramanik T. Integration of multiple cache server scheme for user- based fuzzy logic in content delivery networks. In: Madhumangal Pal, Sovan Samanta, and Anita Pal, editors. Handbook of research on advanced applications of graph theory in modern society. IGI Global; 2020. p. 386–396. [11] Akram M, Ali G, Alshehri NO. A new multi-attribute decision-making method based on m-polar fuzzy soft, rough sets. Symmetry (Basel). 2017;9(11):1–18. [12] Ali G, Akram M, Alcantud JCR. Attributes reductions of bipolar fuzzy relation decision systems. Neural Comput Appl. 2019;32:10051–10071. doi:10.1007/s00521-019-04536-8. [13] Gokmen G, Akinci TC, Tektas M, et al. Evaluation of Student performance in laboratory applica- tions using fuzzy logic. Proc Soc Behav Sci. 2010;2: 902–909. [14] Rashid KA, Amin HU, Rehman ZU. Application of expert system with fuzzy logic in teachers performance evaluation. Int J Adv Comput Sci Appl. 2011;2(2):51–57. [15] Alam J, Pandey MK. A soft computing model for evaluating teachers’ overall performance using fuzzy logic. J Inf Technol Software Eng. 2017;7(2):1–9. [16] Thakre TA, Chaudhari OK, Dhawade N. A fuzzy logic multi-criteria approach for evaluation for teachers’ performance. Adv Fuzzy Math. 2017;12(1):12–145. [17] Moon C, Lee J, Lim S. A performance appraisal and promotion ranking system based on fuzzy logic: a implementation case in military organizations. Appl Soft Comput. 2010;10(2):512–519. [18] Srinivasan S, Jain V, Dharmaja S. Perception-based performance analysis of higher education institutions: a soft computing approach. Soft comput. 2020;24:513–521. [19] Das K, Samanta S, De K, et al. Ranking of educational institutions using fuzzy logic: a mathematical approach. Afrika Matematika. 2020. doi:10.1007/s13370-020-00796-z. [20] Khan SK, Farasat M, Naseem U, et al. Performance evaluation of next-generation wireless (5G) UAV relay, wireless personal communications. Wirel Pers Commun. 2020;113:145–160. [21] Khan SK, Farasat M, Naseem U, et al. Link-level performance modelling for next-generation UAV relay with millimetre-wave simultaneously in access and Backhaul. Indian J Sci Technol. 2019;12(39):1–9. [22] Naseem U, Musial K. Dice: Deep intelligent contextual embedding for Twitter sentiment analysis. 2019 International conference on document analysis and recognition (ICDAR); 2019, 953–958. [23] Naseem U, Khan SK, Razzak I, et al. Hybrid Words Representation for Airlines Sentiment Analysis. Australasian Joint Conference on Artificial Intelligence, 381-392, 2019. [24] Naseem U, Razzak I, Hameed IA. Deep context-aware embedding for abusive and hate speech detection on Twitter. Aust J Intell Inf Process Syst. 2020;15(4):69–76. [25] Naseem U, Razzak I, Musial K, et al. Transformer based deep intelligent contextual embedding for twitter sentiment analysis. Future Gener Comput Syst. 2020;113:58–69. [26] Naseem U, Khan SK, Farasat M, et al. Abusive language detection: a comprehensive review. Indian J Sci Technol. 2019;12(45):1–13. [27] Samanta S, Pal M, Rashmanlou H, et al. Vague graphs and strengths. J Intell Fuzzy Syst. 2016;30(6):3675–3680. [28] Samanta S, Sarkar B. A study on generalized fuzzy graphs. J Intell Fuzzy Syst. 2018;35:3405–3412. [29] Samanta S, Sarkar B. Representation of competitions by generalized fuzzy graphs. Int J Comput Intell Syst. 2018;11:1005–1015. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Fuzzy Information and Engineering Taylor & Francis

Application of Fuzzy Logic in the Ranking of Academic Institutions

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Abstract

FUZZY INFORMATION AND ENGINEERING 2019, VOL. 11, NO. 3, 295–306 https://doi.org/10.1080/16168658.2020.1805253 Application of Fuzzy Logic in the Ranking of Academic Institutions a b c d e Kousik Das , Sovan Samanta , Usman Naseem , Shah Khalid Khan and Kajal De a b Department of Mathematics, D. J. H. School, Dantan, India; Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, India; School of Computer Science, University of Technology Sydney, Sydney, d e Australia; School of Engineering, RMIT University, Carlton, Australia; Department of Mathematics, Netaji Subhas Open University, Kolkata, India ABSTRACT ARTICLE HISTORY Received 11 October 2019 For the development of any organization, evaluation of performance Revised 14 July 2020 is an important task. To analyze the performance, Das et al. intro- Accepted 17 July 2020 duced a ranking framework based on fuzzy logic. That framework compared the current NIRF system of Indian Institutions with the KEYWORDS fuzzy logic-based Mamdani system, KSM index. In that study, uniform Fuzzy control system; NIRF; membership functions are not taken. This study will focus on the KSM index; Sugeno ranking system based on Mamdani and Sugeno with fuzzy triangular numbers as input values of membership functions. Also, the updated results are compared with existing NIRF systems and considered Top 20 institutions of India for the year 2019 as per NIRF. 1. Introduction Education is a basic need for our society and life. The government of India provides qual- ity education to the people for free and compulsory [1] at the primary level. Many higher education institutions in India provide quality education and develop our society. Like eval- uation of students every year, every institution needs to analyze their performances. To compare the performances among institutions, there must need a ranking framework. A most well-known method for ranking higher institutions by MHRD (Govt. of India) is the National Institutional Ranking Framework (NIRF) [2]. Generally, the ranking of Indian institutes is done by NIRF, Govt of India based on crisp weighted data. But, these crisp data sometimes are less significant when grading systems are used. Fuzzy logic is better to represent such linguistic variables as low, medium, or high. Fuzzy logic handles the imprecise and vagueness data. Fuzzy logic, algorithm, and decision making first introduced by L. A. Zadeh [3–6]. After that, E. H. Mamdani [7,8] applied fuzzy logic to control an automatic stream engine. Fuzzy logic [9,10] has been applied in many areas like decision making [11,12] automatic control, banks, hospitals, and academic insti- tutions [13–16]. Moon et al. proposed a model for performance analysis and promotion ranking [17] in military organizations in Korea In [18], Srinivasan et al., introduced percep- tion based performance analysis of higher institutions. In that paper, authors considered CONTACT Sovan Samanta ssamantavu@gmail.com © 2021 The Author(s). Published by Taylor & Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society of China & Operations Research Society of Guangdong Province. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. 296 K. DAS ET AL. students, faculty, research investor, and public as perceptions, and this model is based on various parameters also, but did not survey any real data. In [19], Das et al. introduced the KSM index of ranking educational institutions based on fuzzy systems. In that study, input membership values are assumed as per the weight of the input data as per Mamdani rule-based systems. The crisp result is obtained through the defuzzification of rules’ in the Mamdani system. Combining more than two inputs in crisp data needs lots of rules. For example, if you say teaching got 90% credit, Research got 70%, and Infrastructure got 50% credits. These rules will give an output. At the same time, changing a bit like teaching got 89% credit, Research got 72%, and Infrastructure got 51% credits, the rule will be changed. So infinite numbers of rules are to be prepared. Fuzzy logic is adapted realistically. Rules are limited as the parameters are divided into low, medium, high category or few more. Few more survey can be found in [20–26]. In the current NIRF system, few drawbacks are seen. Crisp weighted results are assumed for ranking. As per data collection, the input values are crisp. But to evaluate teaching- learning, Infrastructure, and research publications, fuzzy credentials are much realistic. Thus, instead of crisp inputs, fuzzy inputs are rather helpful and justified. This problem has been addressed by KSM Index in the paper by Das et al.. In KSM Index, the major drawback is that the inputs are used without uniformity. In our proposed study, the techniques of the KSM Index have been advanced. Besides, the ranking is provided based on Sugeno fuzzy rule-based systems. And finally, a comparison is made with Mamdani, Sugeno, and crisp NIRF methods. To study this, we collected data of the top 20 higher institutes of India as per NIRF 2019 and illustrated the results. The rest of the paper is organized as follows. In section 2, we studied some basic concepts on fuzzy logic and rule base system and NIRF system. In section 3, we proposed our model and discussed and comparing the result with the existing model. In section 4, we conclude the model with future directions. 2. Preliminaries In this section, we studied the basic knowledge of fuzzy logic, fuzzy inference system and existing NIRF system. 2.1. Fuzzy Logic An extension of the classical set is a fuzzy set where each object of the fuzzy set have some degree of membership between the values 0 and 1. Let X be non-empty set, then a fuzzy set Z in X is defined as Z ={x, µ (x) : x ∈ X} where µ (x) is the membership function of x in Z and the value of µ (x) lies between 0 and z z 1insuchawaythat ⎪ 1, x is strongly lies in X µ (x) = z (0, 1), x is partially lies in x 0, x is not in X. FUZZY INFORMATION AND ENGINEERING 297 Figure 1. Membership function of temperature. A mapping from any input set to a degree of membership between 0 and 1 is called a membership function. A triangular membership function is defined as x − a if a ≤ x < b ⎪ b − a 1 if x = b µ (x) = c − x if b ≤ x < c ⎪ c − b 0 otherwise In traditional logic, an element in the set completely belongs to the set or not that is 0 or 1. In the real world, we lead with ambiguities, vague concepts that are smoothly handled by fuzzy logic. It has applications in many fields like automation technology, control, robotics, image processing, medical diagnosis, pattern recognition, etc. To save energy, many fuzzy logic-based home appliances like refrigerators are being invented. Fuzzy logic is associated with an important term linguistic variable. It represents a word like ‘temperature’, ‘age’, etc. where the temperature may be very cool, cool, hot, very hot. So these are actually fuzzy membership functions (Figure 1). For further studies, readers can check the references [27–29]. 2.2. Fuzzy Inference System Fuzzy inference system (FIS) is a complete process that works on a given set of crisp inputs to crisp output based on fuzzy logic. It has four parts that are fuzzification, fuzzy rule base, fuzzy inference, and defuzzification. In fuzzification, all crisp inputs convert into fuzzy linguistic value. Then if-else rules are defined on these linguistic values. After that, all combinations of fuzzy rules with membership functions are performed to produce fuzzy output using AND, OR, NOT, etc. operations. In defuzzification, all fuzzy outputs convert into crisp value by any method (Centroid, MOM, etc.). A diagram for FIS is shown in Figure 2. 298 K. DAS ET AL. Figure 2. FIS system. Table 1. NIRF parameters. Sl. No. Parameters Marks Weightage 1 Teaching, Learning & Resources (TLR) 100 0.30 2 Research and Professional Practice (RPP) 100 0.30 3 Graduation Outcomes (GO) 100 0.20 4 Outreach and Inclusivity (OI) 100 0.10 5 Perception (PR) 100 0.10 2.3. NIRF System To evaluate the performance of the higher institutions in India and ranking the insti- tutions, MHRD approved a system in 2015 called NIRF (National Institutional Ranking Framework). This system of evaluation consists of five major parameters. These are “Teach- ing, Learning and Resources(TLR),’ ‘Research and Professional Practices(RPP),’ ‘Graduation Outcomes(GO),’ ‘Outreach and Inclusivity(OI),’ and ‘Perception(PR)’. The weightage value considers in this system for these parameters are given in the table. NIRF calculates the score of an institution by a weighted sum method. All parameters are summarized following in the table (Table 1). 3. Method for Evaluation of Performance In practical, all input parameters (TLR, RPP, GO, OI, PR) are linguistic terms. So all parameters have linguistic values with some degree of memberships. We design a fuzzy logic rule base system considering these parameters to get the new score. The index has the following brief steps. Algorithm: Input: Percentage of TLR, RPP, GO and PR for each institute. Output: Score of a ranking framework based on a fuzzy logic system. Step- I: Construct all membership functions for all input parameters ‘TLR’, ‘RPP’, ‘GO’, ‘OI’, ‘PR’ as triangular fuzzy numbers and the same for output parameter ‘score’ in Mam- dani/Sugeno FIS. Step-II: Define fuzzy rule base on these parameters. This rule-base follows the rules of NIRF as per the weights. That is the weight ratio for the input parameters are 3:3:2:1:1. FUZZY INFORMATION AND ENGINEERING 299 Figure 3. Membership function for input and output parameter. Table 2. Ranges of input and output parameters. Input/Output Parameter Linguistic values Range TLR, RPP, GO, OI, PR, Score Low (1) (−40, 0, 40) Medium (2) (10, 50, 90) High (3) (60, 100, 140) Step-III: Use Mamdani/Sugeno computation tool for combining membership functions with the fuzzy rules to derive the fuzzy output and finally crisp output. 3.1. Membership Functions The details range of linguistic input parameters and an output parameter (Table 2)aretaken uniformly, and the corresponding membership function (Figure 3) is given below. 3.2. Fuzzy Rule Base In our study, we considered five inputs and one output. Combining all these inputs, we developed all possible 243 IF-THEN rules. All the rules are shown below in Table 3. 3.3. Results and Observations A comparision of inputs (TLR, RP, GO, OI and PR) of academic institutions are shown in Figure 4. We got the score of all institutions as per given inputs (Table 4) using two tools Mamdani and Sugeno. An input and output score of DU is shown in Figure 5.Asurface viewer is shown in Figure 6. The results are compared with the existing model in Table 4. Comparing ranking in all methods for the institutions are shown in Table 5.Agraphical comparison between NIRF and fuzzy logic-based model is shown in Figure 7. We observed from that the results that i. Scores of the assumed institutes based on Sugeno are higher than that of Mamdani. ii. The rank of the top twenty institutes of India according to NIRF method and other two fuzzy logic methods are shown in Table 5. All three methods suggest that IITM and IISC 300 K. DAS ET AL. Table 3. If-Then rule base. Sr. No TLR RP GO OI PR Output Sr. No TLR RP GO OI PR Output 1 1 11 1 1 1 31 1 21 2 1 1 2 1 11 1 2 1 32 1 21 2 2 2 3 1 11 1 3 1 33 1 21 2 3 2 4 1 11 2 1 1 34 1 21 3 1 2 5 1 11 2 2 1 35 1 21 3 2 2 6 1 11 2 3 1 36 1 21 3 3 2 7 1 11 3 1 1 37 1 22 1 1 1 8 1 11 3 2 2 38 1 22 1 2 2 9 1 11 3 3 2 39 1 22 1 3 2 10 1 1 2 1 1 1 40 1 2 2 2 1 2 11 1 1 2 1 2 1 41 1 2 2 2 2 2 12 1 1 2 1 3 1 42 1 2 2 2 3 2 13 1 1 2 2 1 1 43 1 2 2 3 1 2 14 1 1 2 2 2 1 44 1 2 2 3 2 2 15 1 1 2 2 3 2 45 1 2 2 3 3 2 16 1 1 2 3 1 2 46 1 2 3 1 1 2 17 1 1 2 3 2 2 47 1 2 3 1 2 2 18 1 1 2 3 3 2 48 1 2 3 1 3 2 19 1 1 3 1 1 1 49 1 2 3 2 1 2 20 1 1 3 1 2 2 50 1 2 3 2 2 2 21 1 1 3 1 3 2 51 1 2 3 2 3 2 22 1 1 3 2 1 2 52 1 2 3 3 1 2 23 1 1 3 2 2 2 53 1 2 3 3 2 2 24 1 1 3 2 3 2 54 1 2 3 3 3 3 25 1 1 3 3 1 2 55 1 3 1 1 1 1 26 1 1 3 3 2 2 56 1 3 1 1 2 2 27 1 1 3 3 3 2 57 1 3 1 1 3 2 28 1 2 1 1 1 1 58 1 3 1 2 1 2 29 1 2 1 1 2 1 59 1 3 1 2 2 2 30 1 2 1 1 3 1 60 1 3 1 2 3 2 Sr. No TLR RP GO OI PR Output Sr. No TLR RP GO OI PR Output 61 1 3 1 3 1 2 92 2 1 2 1 2 1 62 1 3 1 3 2 2 93 2 1 2 1 3 2 63 1 3 1 3 3 2 94 2 1 2 2 1 2 64 1 3 2 1 1 2 95 2 1 2 2 2 2 65 1 3 2 1 2 2 96 2 1 2 2 3 2 66 1 3 2 1 3 2 97 2 1 2 3 1 2 67 1 3 2 2 1 2 98 2 1 2 3 2 2 68 1 3 2 2 2 2 99 2 1 2 3 3 2 69 1 3 2 2 3 2 100 2 1 3 1 1 2 70 1 3 2 3 1 2 101 2 1 3 1 2 2 71 1 3 2 3 2 2 102 2 1 3 1 3 2 72 1 3 2 3 3 3 103 2 1 3 2 1 2 73 1 3 3 1 1 2 104 2 1 3 2 2 2 74 1 3 3 1 2 2 105 2 1 3 2 3 2 75 1 3 3 1 3 2 106 2 1 3 3 1 2 76 1 3 3 2 1 2 107 2 1 3 3 2 2 77 1 3 3 2 2 3 108 2 1 3 3 3 3 78 1 3 3 2 3 3 109 2 2 1 1 1 1 79 1 3 3 3 1 2 110 2 2 1 1 2 2 80 1 3 3 3 2 3 111 2 2 1 1 3 2 81 1 3 3 3 3 3 112 2 2 1 2 1 2 82 2 1 1 1 1 1 113 2 2 1 2 2 2 83 2 1 1 1 2 1 114 2 2 1 2 3 2 84 2 1 1 1 3 2 115 2 2 1 3 1 2 85 2 1 1 2 1 2 116 2 2 1 3 2 2 86 2 1 1 2 2 2 117 2 2 1 3 3 2 87 2 1 1 2 3 2 118 2 2 2 1 1 2 88 2 1 1 3 1 2 119 2 2 2 1 2 2 89 2 1 1 3 2 2 120 2 2 2 1 3 2 (continued) FUZZY INFORMATION AND ENGINEERING 301 Table 3. Continued. Sr. No TLR RP GO OI PR Output Sr. No TLR RP GO OI PR Output 90 2 1 1 3 3 2 121 2 2 2 2 1 2 91 2 1 2 1 1 1 122 2 2 2 2 2 2 Sr. No TLR RP GO OI PR Output Sr. No TLR RP GO OI PR Output 123 2 2 2 2 3 2 154 2 3 3 1 1 2 124 2 2 2 3 1 2 155 2 3 3 1 2 2 125 2 2 2 3 2 2 156 2 3 3 1 3 2 126 2 2 2 3 3 3 157 2 3 3 2 1 2 127 2 2 3 1 1 2 158 2 3 3 2 2 2 128 2 2 3 1 2 2 159 2 3 3 2 3 3 129 2 2 3 1 3 2 160 2 3 3 3 1 2 130 2 2 3 2 1 2 161 2 3 3 3 2 3 131 2 2 3 2 2 2 162 2 3 3 3 3 3 132 2 2 3 2 3 2 163 3 1 1 1 1 1 133 2 2 3 3 1 2 164 3 1 1 1 2 2 134 2 2 3 3 2 3 165 3 1 1 1 3 2 135 2 2 3 3 3 3 166 3 1 1 2 1 2 136 2 3 1 1 1 1 167 3 1 1 2 2 2 137 2 3 1 1 2 2 168 3 1 1 2 3 2 138 2 3 1 1 3 2 169 3 1 1 3 1 2 139 2 3 1 2 1 2 170 3 1 1 3 2 2 140 2 3 1 2 2 2 171 3 1 1 3 3 2 141 2 3 1 2 3 2 172 3 1 2 1 1 2 142 2 3 1 3 1 2 173 3 1 2 1 2 2 143 2 3 1 3 2 2 174 3 1 2 1 3 2 144 2 3 1 3 3 2 175 3 1 2 2 1 2 145 2 3 2 1 1 2 176 3 1 2 2 2 2 146 2 3 2 1 2 2 177 3 1 2 2 3 2 147 2 3 2 1 3 2 178 3 1 2 3 1 2 148 2 3 2 2 1 2 179 3 1 2 3 2 2 149 2 3 2 2 2 2 180 3 1 2 3 3 3 150 2 3 2 2 3 2 181 3 1 3 1 1 2 151 2 3 2 3 1 2 182 3 1 3 1 2 2 152 2 3 2 3 2 2 183 3 1 3 1 3 2 153 2 3 2 3 3 3 184 3 1 3 2 1 2 Sr. No TLR RP GO OI PR Output Sr. No TLR RP GO OI PR Output 185 3 1 3 2 2 2 216 3 2 3 3 3 3 186 3 1 3 2 3 3 217 3 3 1 1 1 2 187 3 1 3 3 1 2 218 3 3 1 1 2 2 188 3 1 3 3 2 3 219 3 3 1 1 3 2 189 3 1 3 3 3 3 220 3 3 1 2 1 2 190 3 2 1 1 1 2 221 3 3 1 2 2 2 191 3 2 1 1 2 2 222 3 3 1 2 3 2 192 3 2 1 1 3 2 223 3 3 1 3 1 2 193 3 2 1 2 1 2 224 3 3 1 3 2 2 194 3 2 1 2 2 2 225 3 3 1 3 3 3 195 3 2 1 2 3 2 226 3 3 2 1 1 2 196 3 2 1 3 1 2 227 3 3 2 1 2 2 197 3 2 1 3 2 2 228 3 3 2 1 3 3 198 3 2 1 3 3 3 229 3 3 2 2 1 2 199 3 2 2 1 1 2 230 3 3 2 2 2 3 200 3 2 2 1 2 2 231 3 3 2 2 3 3 201 3 2 2 1 3 2 232 3 3 2 3 1 3 202 3 2 2 2 1 2 233 3 3 2 3 2 3 203 3 2 2 2 2 2 234 3 3 2 3 3 3 204 3 2 2 2 3 2 235 3 3 3 1 1 2 205 3 2 2 3 1 2 236 3 3 3 1 2 3 206 3 2 2 3 2 3 237 3 3 3 1 3 3 207 3 2 2 3 3 3 238 3 3 3 2 1 3 208 3 2 3 1 1 2 239 3 3 3 2 2 3 209 3 2 3 1 2 2 240 3 3 3 2 3 3 (continued) 302 K. DAS ET AL. Table 3. Continued. Sr. No TLR RP GO OI PR Output Sr. No TLR RP GO OI PR Output 210 3 2 3 1 3 3 241 3 3 3 3 1 3 211 3 2 3 2 1 2 242 3 3 3 3 2 3 212 3 2 3 2 2 3 243 3 3 3 3 3 3 213 3 2 3 2 3 3 214 3 2 3 3 1 3 215 3 2 3 3 2 3 Figure 4. Comparision of inputs. Figure 5. Score of DU. FUZZY INFORMATION AND ENGINEERING 303 Figure 6. Surface viewer. Figure 7. Graphical comparison among all models. are top two institutes in India. Again, the lowest spot among the top twenty is fixed to DU. iii. Figure 7 shows the comparative graphs of all three methods. Result of ranking based on NIRF and Mamdani is similar. The changes in the ranking are low, while the other method based on Sugeno has a significant difference. 304 K. DAS ET AL. Table 4. Input and output for all models. Sr. No. INSTITUTE TLR RP GO OI PR NIRF Sugeno Mamdani 1 IITM 84.57 83.54 87.13 66.08 94.14 83.88 97.2 71.7 2 IISC 83.16 89.24 78.56 50.69 86.92 82.28 94.4 67.4 3 IITD 78.3 82.98 79.13 58.58 86.14 78.69 86.2 62.9 4 IITB 76.95 84.37 82.32 50.69 86.92 78.62 88.7 65.2 5 IITKGP 67.35 76.65 86.17 60.63 78.11 74.31 82.7 60.5 6 IITK 71.96 69.61 69.96 50.39 75.68 69.07 62.6 55.6 7 JNU 76.75 41.85 99.87 75.87 55.27 68.68 89.6 60.2 8 IITR 67.32 65.08 87.14 61.64 43.66 67.68 63.2 53.1 9 IITG 76.8 56.58 73.87 60.63 46.34 65.47 63.5 57.9 10 BHU 69.72 46.48 96.37 57.02 47.28 64.55 66.2 54.5 11 HU 74.81 43.77 83.65 58.77 36.71 61.85 67.3 58.6 12 CU 62.26 47.1 91.54 60.14 37.39 60.87 53.6 50.7 13 JU 54.39 54.89 90.28 44.95 51.83 60.53 50 50 14 AU 56.39 54.09 78.07 53.16 62.72 60.35 52.7 50 15 AVV 73.02 43.77 70.28 70.23 31.01 59.22 61.7 55.5 16 MAHE 77.9 38.32 69.71 66.78 30.21 58.50 60.7 55.1 17 SPPU 69.25 44.42 86.04 54.33 16.55 58.40 52.9 53 18 AMU 76.69 35.38 85.66 57.57 18.46 58.36 55.7 54.6 19 JMI 73.75 32.04 88.53 71.97 14.26 58.07 59.2 56.7 20 DU 47.86 53.8 87.18 55.41 41.11 57.59 50 50 Table 5. Comparison of ranking for all models. Ranking NIRF(2019) Sugeno Mamdani 1 IITM IITM IITM 2 IISC IISC IISC 3 IITD JNU IITB 4 IITB IITB IITD 5 IITKGP IITD IITKGP 6 IITK IITKGP JNU 7 JNU HU HU 8 IITR BHU IITG 9 IITG IITG JMI 10 BHU IITR IITK 11 HU IITK AVV 12 CU AVV MAHE 13 JU MAHE AMU 14 AU JMI BHU 15 AVV AMU IITR 16 MAHE CU SPPU 17 SPPU SPPU CU 18 AMU AU JU 19 JMI JU AU 20 DU DU DU iv. Figure 7 also indicates that the ranking based on Mamdani and Sugeno is proportional. That means the peaks are at the same points. 4. Conclusion In the decision making and evaluation process, fuzzy logic has enormous applications. In this study, a fuzzy logic-based model for ranking higher institutions is proposed in both Mamdani and Sugeno tools. This study captures all real inputs and found a realistic result better from the crisp model. This study concludes that the results based on fuzzy logic are practical. In Sugeno, results are directly related to the crisp numbers, but in Mamdani, the FUZZY INFORMATION AND ENGINEERING 305 results are obtained due to defuzzification. Thus it is advisable to choose the consequences of Mamdani based system. The difference between the ranking is shown in Table 5 and Figure 7. Many companies and organizations are always finding the best evaluation tools for their performance analysis. In the future, the proposed model will be beneficial for all others rank- ing such as companies, publishers, countries, etc. to evaluate their performance. This type of ranking should apply to find the top institute to provide financial help, research grant, etc. to the sponsoring authority. Disclosure statement No potential conflict of interest was reported by the author(s). Notes on contributors Mr. Kousik Das has 3 years of research experience in graph theory, fuzzy graph theory and social net- works. He is working as a teacher at D.J.H. School, Dantan, West Bengal, India. He has published 10 articles and book chapters in Springer, IEEE Explore, IGI global, NSS, Hindawi publishers. Dr. Sovan Samanta is an Assistant Professor in the Department of Mathematics, Tamralipta Mahavidyalaya (Vidyasagar University). He worked as Assistant Professor in Indian Institute of Infor- mation Technology, Nagpur. He was a post-doc fellow at Hanyang University, Ansan, South Korea. He completed his Ph.D. from Vidyasagar University in Fuzzy Graph Theory. He introduced fuzzy planar graphs, fuzzy competition graphs, fuzzy tolerance graphs, etc. He published more than 60 articles in different reputed SCI/SCIE and Scopus Journals. His current research interests include data science, graph theory, social networks, and fuzzy graphs. Mr. Usman Naseem has received Master of Analytics (research) from Advanced Analytics Institute, University of Technology, Sydney, Australia in 2020. Currently, he is pursuing Ph.D in computer sci- ence. He has published several papers in well-reputed journals and conferences. His area of research includes social data analytics, natural language processing, health-care analytics and machine learn- ing. Mr. Shah Khalid Khan is a research scholar at RMIT University, Melbourne, Australia. He is a quali- fied ICT professional, having worked with multinational telecom vendors and operators in multiple domains for more than 08 years after doing B.E (Electrical Engineering) in 2008. He completed master by research degree from RMIT University, Melbourne, Australia. His research interests include next generation wireless networks, millimeter-wave technology, Connected and Autonomous Vehicles (CAVs), cybersecurity, data science, data analytics and machine learning techniques. Dr. Kajal De is a professor in the Department of Mathematics, Netaji Subhas Open University, India. 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Journal

Fuzzy Information and Engineering – Taylor & Francis

Published: Jul 3, 2019

Keywords: Fuzzy control system; NIRF; KSM index; Sugeno

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