INFORMATION MEASURES BASED TOPSIS METHOD FOR MULTICRITERIA DECISION MAKING PROBLEM IN INTUITIONISTIC FUZZY ENVIRONMENT

Document Type : Research Paper

Authors

1 Department of Mathematics, ITM University, Gwalior- 474001, M. P., India

2 Department of Mathematics, Jaypee University of Engineering and Technology, Guna-473226, M. P., India

Abstract

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.

Keywords


[1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[39] E. Szmidt and J. Kacprzyk, Entropy for Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems,
118 (2011), 467-477.
[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.
[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.
[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.
[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.
[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.
[49] Z. H. Xu, J. Chen and J. J.Wu, Clustering algorithm for intuitionistic fuzzy sets, Information
Sciences, 178 (2008), 37753790.
[50] Z. S. Xu and Q. L. Da, The ordered weighted geometric averaging operators, International
Journal of Intelligent Systems, 17 (2002), 709716.
[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.
[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.