A comparison of the performance of entropy measures for interval-valued intuitionistic fuzzy sets

Yıl 2021, Cilt: 39 Sayı: 2, 131 - 147, 02.06.2021

Melda Kokoç Süleyman Ersöz

Öz

Entropy measure is a significant tool to define unclear information. But, entropy measures for interval-valued intuitionistic fuzzy sets (IVIFSs) cannot be easily understood intuitively. So, it is highly important to compare the existing measures to select a reliable entropy measure in studies. The purpose of this study is to compare the performance of different entropy measures developed for IVIFSs. The numerical examples are presented to show whether entropy measures for IVIFSs are effective in representing the fuzziness degree. In order to understand whether a variation of fuzziness degree of one or more elements of IVIFSs change the ranking results, selected IVIFSs are modified diversely.

Anahtar Kelimeler

Entropy, interval-valued intuitionistic fuzzy sets, performance test

Kaynakça

• [1] Zadeh L.A. Fuzzy sets, Information and Control 1965; 8(3):338-353.
• [2] Atanassov K. Intuitionistic fuzzy sets, Fuzzy Sets and Systems 1986; 20 (1):87–96.
• [3] Atanassov K. More on intuitionistic fuzzy sets. Fuzzy Sets and Systems 1989; 33(1):37-45.
• [4] Pedrycz, W. Granular computing: analysis and design of intelligent systems. CRC Press; 2018.
• [5] Liu, Y., Jiang, W. A new distance measure of interval-valued intuitionistic fuzzy sets and its application in decision making. Soft Computing 2019; 1-17.
• [6] Li, D. F. Extension principles for interval-valued intuitionistic fuzzy sets and algebraic operations. Fuzzy Optimization and Decision Making 2011;10(1): 45-58.
• [7] Chen, T. Y. Interval-valued intuitionistic fuzzy QUALIFLEX method with a likelihood-based comparison approach for multiple criteria decision analysis. Information Sciences 2014; 261:149-169.
• [8] Chen, T. Y. IVIF-PROMETHEE outranking methods for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets. Fuzzy Optimization and Decision Making 2015;14(2):173-198.
• [9] Park, J. H., Cho, H. J., Kwun, Y. C. Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information. Fuzzy Optimization and Decision Making 2011; 10(3): 233-253.
• [10] Kacar, S., Eksi, Z., Akgul, A., Horasan, F. MATLAB paralel hesaplama araç kutusu ile shannon entropi hesaplanmasi. 1st Internatonal Symposum on Innovatve Technologes in Engneerng and Science 2013; 765-773.
• [11] Zhang, Q. S., Jiang, S. Y., Jia, B. G., Luo, S. H. Some information measures for interval-valued intuitionistic fuzzy sets. Information Sciences 2010;180:5130–5145.
• [12] Burillo, P., Bustince, H. Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy sets and systems 1996; 78(3): 305-316.
• [13] Liu, X. D., Zheng, S. H., Xiong, F. L. Entropy and subsethood for general interval-valued intuitionistic fuzzy sets. In International Conference on Fuzzy Systems and Knowledge Discovery, Springer, Berlin, Heidelberg, 2005.
• [14] Wei, C. P., Wang, P., Zhang, Y. Z. Entropy, similarity measure for inter- val-valued intuitionistic fuzzy sets and their application. Information Sciences 2011;181(19): 4273–4286.
• [15] Gao, Z.,Wei, C. Formula of interval-valued intuitionistic fuzzy entropy and its applications. Jisuanji Gongcheng yu Yingyong(Computer Engineering and Applications) 2012;48(2): 53–55.
• [16] Jin, F., Pei, L., Chen, H., Zhou, L. Interval-valued intuitionistic fuzzy continuous weighted entropy and its application to multi-criteria fuzzy group decision making. Knowledge-Based Systems 2014;59:132-141.
• [17] Zhang, Q., Jiang, S. Relationships between entropy and similarity measure of interval‐valued intuitionistic fuzzy sets. International Journal of Intelligent Systems 2010; 25(11):1121-1140.
• [18] De Luca, A., Termini, S. A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Information and control 1972; 20(4): 301-312.
• [19] Zhang, Y. J., Ma, P. J., Su, X. H., Zhang, C. P. Entropy on interval-valued intuitionistic fuzzy sets and its application in multi-attribute decision making. In Proceedings of the 14th international conference on information fusion (FUSION) 2011; 1121–1140.
• [20] Zhang, Q., Xing, H., Liu, F., Ye, J., Tang, P. Some new entropy measures for interval-valued intuitionistic fuzzy sets based on distances and their relation- ships with similarity and inclusion measures. Information Sciences 2014; 283: 55–69.
• [21] Rashid, T., Faizi, S., Zafar, S. Distance Based Entropy Measure of Interval-Valued Intuitionistic Fuzzy Sets and Its Application in Multicriteria Decision Making. Advances in Fuzzy Systems, 2018.
• [22] Xian, S., Dong, Y., Liu, Y., Jing, N. A novel approach for linguistic group decision making based on generalized interval‐valued intuitionistic fuzzy linguistic induced hybrid operator and TOPSIS. International Journal of Intelligent Systems 2018; 33(2): 288-314.
• [23] Tiwari, P., Gupta, P. Entropy, distance and similarity measures under interval valued intuitionistic fuzzy environment. Informatica 2018; 42:617-627.
• [24] Mishra, A. R., Rani, P., Pardasani, K. R., Mardani, A., Stević, Ž., Pamučar, D. A novel entropy and divergence measures with multi-criteria service quality assessment using interval-valued intuitionistic fuzzy TODIM method. Soft Computing, 2020; 24:11641–11661.
• [25] Ye, J. Fuzzy cross entropy of interval-valued intuitionistic fuzzy sets and its optimal decision-making method based on the weights of alternatives. Expert Systems with Applications 2011; 38(5): 6179-6183.
• [26] Chen, X., Yang, L., Wang, P., Yue, W. A fuzzy multi-criteria group decision–making method with new entropy of interval-valued intuitionistic fuzzy sets. Journal of Applied Mathematics, 2013, 1–8.
• [27] Meng, F., Tang, J. Interval‐valued intuitionistic fuzzy multiattribute group decision making based on cross entropy measure and Choquet integral. International Journal of Intelligent Systems 2013; 28(12): 1172-1195.
• [28] Zhang, Y., Li, P., Wang, Y., Ma, P., Su, X. Multiattribute decision making based on entropy under interval-valued intuitionistic fuzzy environment. Mathematical Problems in Engineering, 2013.
• [29] Wei, C., Zhang, Y. Entropy measure for interval-valued intuitionistic fuzzy sets and their application in group decision-making. Mathematical problems in engineering 2015.
• [30] Nguyen, H. A new interval-valued knowledge measure for interval-valued intuitionistic fuzzy sets and application in decision making. Expert Systems with Applications 2016; 56: 143-155.
• [31] Liu, P., Qin, X. An extended VIKOR method for decision making problem with interval-valued linguistic intuitionistic fuzzy numbers based on entropy. Informatica 2017; 28(4): 665-685.
• [32] Zhao, H., You, J. X.,Liu, H. C. Failure mode and effect analysis using MULTIMOORA method with continuous weighted entropy under interval-valued intuitionistic fuzzy environment. Soft Computing 2017; 21(18): 5355-5367.
• [33] Xu, Z. Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis 2017; 22(2):215–219.
• [34] Bustince, H., Burillo, P. Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy sets and systems, 1995; 74(2): 237-244.
• [35] Bustince Sola, H., Burillo López, P. A theorem for constructing interval-valued intuitionistic fuzzy sets from intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets 1 1995;5-16.
• [36] Atanassov, K. T. (1994). Operators over interval valued intuitionistic fuzzy sets. Fuzzy sets and systems, 64(2), 159-174.
• [37] Xu, Z., Chen, J. On geometric aggregation over interval-valued intuitionistic fuzzy information. In Fourth international conference on fuzzy systems and knowledge discovery (FSKD 2007) 2007; 2: 466-471.
• [38] Xu, Z., Chen, J. Approach to group decision making based on interval-valued intuitionistic judgment matrices. Systems Engineering-Theory & Practice 2007;27(4):126-133.
• [39] Ye, J. Multicriteria fuzzy decision-making method using entropy weight- s-based correlation coefficients of interval-valued intuitionistic fuzzy sets. Applied Mathematical Modelling 2010; 34 (24): 3864–3870.
• [40] Sun, M., Liu, J. New entropy and similarity measures for interval-valued intuitionistic fuzzy sets. Journal of Information &Computational Science 2012; 9(18): 5799-5806.
• [41] Jing, L. Entropy and similarity measures for interval-valued intuitionistic fuzzy sets based on intuitionism and fuzziness. Advanced Modeling and Optimization 2013;15 (3): 635–643.
• [42] Chen, X., Yang, L., Wang, P., Yue, W. An effective interval-valued intuitionistic fuzzy entropy to evaluate entrepreneurship orientation of online P2P lending platforms. Advances in Mathematical Physics, 2013.
• [43] Guo, K., Song, Q. On the entropy for Atanassov's intuitionistic fuzzy sets: An interpretation from the perspective of amount of knowledge. Applied Soft Computing 2014; 24: 328-340.
• [44] Xu, J., Shen, F. A new outranking choice method for group decision making under Atanassov’s interval-valued intuitionistic fuzzy environment. Knowledge-Based Systems 2014; 70:177-188.
• [45] Zhao, N., Xu, Z. Entropy measures for interval-valued intuitionistic fuzzy information from a comparative perspective and their application to decision making. Informatica 2016; 27(1): 203-229.
• [46] Rani, P., Jain, D., Hooda, D. S. Shapley function based interval-valued intuitionistic fuzzy VIKOR technique for correlative multi-criteria decision making problems. Iranian Journal of Fuzzy Systems 2018;15(1): 25-54.
• [47] Guo, K., Zang, J. Knowledge measure for interval-valued intuitionistic fuzzy sets and its application to decision making under uncertainty. Soft Computing 2019; 23(16): 6967-6978.