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Information measures based TOPSIS method for multicriteria decision making problem in intuitionistic fuzzy environment. (English) Zbl 1398.91196

Summary: In the fuzzy set theory, information measures play a paramount role in several areas such as decision making, pattern recognition etc. In this paper, similarity measure based on cosine function and entropy measures based on logarithmic function for IFSs are proposed. Comparisons of proposed similarity and entropy measures with the existing ones are listed. Numerical results limpidly betoken the efficiency of these measures over others. An intuitionistic fuzzy weighted measures (IFWM) with TOPSIS method for multi-criteria decision making (MCDM) quandary is introduced to grade the alternatives. This approach is predicated on entropy and weighted similarity measures for IFSs. An authentic case study is discussed to rank the four organizations. To compare the different rankings, a portfolio selection problem is considered. Various portfolios have been constructed and analysed for their risk and return. It has been examined that if the portfolios are developed using the ranking obtained with proposed method, the return is increased with slight increment in risk.

MSC:

91B06 Decision theory
94A17 Measures of information, entropy
03E72 Theory of fuzzy sets, etc.
90B50 Management decision making, including multiple objectives
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[1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96. · Zbl 0631.03040
[2] P. Burillo and H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems, 78 (1996), 305-316. · Zbl 0872.94061
[3] C. T. Chen, Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets and Systems, 114 (2000), 01-09.
[4] A. De Luca and S. Termini, A de nition of non-probabilistic entropy in the setting of fuzzy set theory, Inform. and Control, 20 (1972), 301-312. · Zbl 0239.94028
[5] S. Ebrahimnejad, H. Hashemi, S. M. Mousavi and B. Vahdani, A new interval-valued intu- itionistic fuzzy model to group decision making for the selection of outsourcing providers, Journal of Economic Computation and Economic Cybernetics Studies and Research, 49 (2015), 269-290.
[6] P. Grzegorzewski, On possible and necessary inclusion of intuitionistic fuzzy sets, Information Sciences, 181 (2011), 342-350. · Zbl 1214.03038
[7] D. S. Hooda and A. R. Mishra, On trigonometric fuzzy information measures, ARPN Journal of Science and Technology, 05 (2015), 145-152.
[8] D. S. Hooda, A. R. Mishra and D. Jain, On generalized fuzzy mean code word lengths, American Journal of Applied Mathematics, 02 (2014), 127-134.
[9] C. C. Hung and L. H. Chen, A fuzzy TOPSIS decision making model with entropy weight under intuitionistic fuzzy environment, In: Proceedings of the international multi conference of engineers and computer scientists (IME CS-2009), 01 (2009), 13-16.
[10] W. L. Hung and M. S. Yang, Fuzzy entropy on intuitionistic fuzzy sets, International Journal of Intelligent Systems, 21 (2006), 443-451. · Zbl 1091.94012
[11] W. L. Hung and M. S. Yang, On similarity measures between intuitionistic fuzzy sets, Inter- national Journal of Intelligent Systems, 23 (2008), 364-383. · Zbl 1136.03327
[12] W. L. Hung and M. S. Yang, Similarity measures of intuitionistic fuzzy sets based on Haus- dor distance, Pattern Recognition Letters, 25 (2004), 1603-1611.
[13] C. L. Hwang and K. S. Yoon, Multiple attribute decision making: methods and applications, Berlin: Springer-Verlag, 1981. · Zbl 0453.90002
[14] D. Joshi and S. Kumar, Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making, Egyptian informatics journal, 15 (2014), 97-104.
[15] A. Jurio, D. Paternain, H. Bustince, C. Guerra and G. Beliakov, A construction method of attanassov’s intuitionistic fuzzy sets for image processing, In: Proceedings of the Fifth IEEE Conference on Intelligent Systems, 01 (2010), 337-342.
[16] D. F. Li, Relative ratio method for multiple attribute decision making problems, International Journal of Information Technology & Decision Making, 08 (2010), 289-311. · Zbl 1178.90185
[17] D. Li and C. Cheng, New similarity measures of intuitionistic fuzzy sets and application to pattern recognition, Pattern Recognition Letters, 23 (2003), 221-225. · Zbl 0996.68171
[18] J. Li, G. Deng, H. Li and W. Zeng, The relationship between similarity measure and entropy of intuitionistic fuzzy sets, Information Science, 188 (2012), 314-321. · Zbl 1257.03082
[19] F. Li, Z. H. Lu and L. J. Cai, The entropy of vague sets based on fuzzy sets, J. Huazhong Univ. Sci. Tech., 31 (2003), 24-25.
[20] Z. Z. Liang and P. F. Shi, Similarity measures on intuitionistic fuzzy sets, Pattern Recognition Letters, 24 (2003), 2687-2693. · Zbl 1091.68102
[21] L. Lin, X. H. Yuan and Z. Q. Xia, Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets, J. Comp. Syst. Sci., 73 (2007), 84-88. · Zbl 1178.68541
[22] H. W. Liu and G. J. Wang, Multi-criteria decision-making methods based on intuitionistic fuzzy sets, European Journal of Operational Research, 179 (2007), 220-233. · Zbl 1163.90558
[23] H. M. Markowitz, Foundations of portfolio theory, J. Finance, 469 (1991), 469-471.
[24] H. M. Markowitz, Portfolio selection, J. Finance, 01 (1952), 77-91.
[25] A. R. Mishra, Intuitionistic fuzzy information measures with application in rating of township development, Iranian Journal of Fuzzy Systems, 13(3) (2016), 49-70. · Zbl 1416.94087
[26] A. R. Mishra, D. Jain and D. S. Hooda, Exponential intuitionistic fuzzy information measure with assessment of service quality, International journal of fuzzy systems, 19(3) (2017), 788- 798.
[27] A. R. Mishra, D. Jain and D. S. Hooda, Intuitionistic fuzzy similarity and information mea- sures with physical education teaching quality assessment, Proceedings of the Second Inter- national Conference on Computer and Communication Technologies, Advances in Intelligent Systems and Computing, 379 (2016), 387-399.
[28] A. R. Mishra, D. Jain and D. S. Hooda, On fuzzy distance and induced fuzzy information measures, Journal of Information and Optimization Sciences, 37 (2) (2016), 193-211.
[29] A. R. Mishra, D. Jain and D. S. Hooda, On logarithmic fuzzy measures of information and discrimination, Journal of Information and Optimization Sciences, 37 (2) (2016), 213-231.
[30] A. R. Mishra, D. S. Hooda and D. Jain, On exponential fuzzy measures of i–07.
[31] A. R. Mishra, D. S. Hooda and D. Jain, Weighted trigonometric and hyperbolic fuzzy infor- mation measures and their applications in optimization principles, International Journal Of Computer And Mathematical Sciences, 03 (2014), 62-68.
[32] H. B. Mitchell, On the Dengfeng-Chuntian similarity measure and its application to pattern recognition, Pattern Recognition Letters, 24 (2003), 3101-3104.
[33] S. M. Mousavi, H. Gitinavard and B. Vahdani, Evaluating construction projects by a new group decision-making model based on intuitionistic fuzzy logic concepts, International Jour- nal of Engineering, 28 (2015), 1313-1319.
[34] S. M. Mousavi and B. Vahdani, Cross-docking location selection in distribution systems: a new intuitionistic fuzzy hierarchical deci–109.
[35] S. M. Mousavi, S. Mirdamadi, S. Siadat, J. Dantan and R. Tavakkoli-Moghaddam, An intu- itionistic fuzzy grey model for selection problems with an application to the inspection plan- ning in manufacturing rms, Engineering Applications of Arti cial Intelligence, 39 (2015), 157167.
[36] S. M. Mousavi, B. Vahdani and S. Sadigh Behzadi, Designing a model of intuitionistic fuzzy VIKOR in multi-attribute group decision-making problems, Iranian Journal of Fuzzy Systems, 13(1) (2016), 4565.
[37] O. Parkash, P. K. Sharma and R. Mahajan, New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle, Information Sciences, 178 (2008), 2389􀀀2395. · Zbl 1172.94661
[38] B. Soylu, Integrating PROMETHEE II with tchebyche function for multi criteria decision making, International Journal of Information Technology & Decision Making, 09 (2010), 525-545. · Zbl 1200.90107
[39] E. Szmidt and J. Kacprzyk, Entropy for Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 118 (2011), 467-477. · Zbl 1045.94007
[40] B. Vahdani, M. Salimi and S. M. Mousavi, A new compromise decision making model based on TOPSIS and VIKOR for solving multi-objective large-scale programming problems with a block angular structure under uncertainty, International Journal of Engineering Transactions B: Applications, 27 (2014), 1673􀀀1680.
[41] I. K. Vlachos and G. D. Sergiagis, Intuitionistic fuzzy information { Application to pattern recognition, Pattern Recognition Lett., 28 (2007), 197-206.}
[42] X. Z. Wang, B. De Baets and E. Kerre, A comparative study of similarity measures, Fuzzy Sets and Systems, 73 (1995), 259-268. · Zbl 0852.04011
[43] P. Z. Wang, Fuzzy Sets and Its Applications, Shanghai Science and Technology Press, Shang- hai, 1983.
[44] C. P. Wei and Y. Zhang, Entropy measures for interval-valued intuitionistic fuzzy sets and their application in group decision making, Mathematical Problems in Engineering, Article ID 563745, 2015 (2015), 01􀀀13. · Zbl 1393.03043
[45] C. P. Wei, P. Wang and Y. Zhang, Entropy, similarity measure of interval-valued intuition- istic fuzzy sets and their applications, Information Sciences, 181 (2011), 4273-4286. · Zbl 1242.03082
[46] Z. B.Wu and Y. H. Chen, The maximizing deviation method for group multiple attribute deci- sion making under linguistic environment, Fuzzy Sets and Systems, 158 (2007), 1608-1617. · Zbl 1301.91014
[47] M. M. Xia and Z. S. Xu, Entropy/cross entropy-based group decision making under intu- itionistic fuzzy environment, Information Fusion, 13 (2012), 31-47.
[48] Z. H. Xu, Intuitionistic preference relations and their application in group decision making, Information Sciences, 177 (2007), 2363-2379. · Zbl 1286.91043
[49] Z. H. Xu, J. Chen and J. J.Wu, Clustering algorithm for intuitionistic fuzzy sets, Information Sciences, 178 (2008), 37753790. · Zbl 1256.62040
[50] Z. S. Xu and Q. L. Da, The ordered weighted geometric averaging operators, International Journal of Intelligent Systems, 17 (2002), 709716. · Zbl 1016.68110
[51] Z. S. Xu and X. Q. Cai, Non linear optimization models for multiple attribute group decision making with intuitionistic fuzzy information, International Journal of Intelligent Systems, 25 (2010), 489513.
[52] R. R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions on Systems, Man, and Cybernetics, 18 (1988), 183190. · Zbl 0637.90057
[53] J. Ye, Two e ective measures of intuitionistic fuzzy entropy, Computing, 87 (2010), 5562.
[54] J. Ye, Fuzzy decision-making method based on the weighted correlation coecient under intuitionistic fuzzy environment, European Journal of Operational Research, 205 (2010), 202204.
[55] Z. Yue, Extension of TOPSIS to determine weight of decision maker for group decision making problems with uncertain information, Exp. Syst. Appl., 39 (2012), 63436350.
[56] L. A. Zadeh, Fuzzy sets, Information and Control, 08 (1965), 338353.
[57] L. A. Zadeh, Is there a need for fuzzy logic?, Information Sciences, 178 (2008), 27512779. · Zbl 1148.68047
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