Correlation Coefficient Based Extended VIKOR Approach Under Intuitionistic Fuzzy Environment

10.6186/IJIMS.202203_33(1).0003

Rakhi Gupta；Satish Kumar

Renyi's ； Intuitionistic fuzzy set(IFSs) ； MCDM (Multi-criteria Decision Making) ； Intuitionistic fuzzy numbers (IFNs) ； VIKOR(Vlsekriterijumska Optimizacija i Kompromisno Resenje) ； Shannon's

International Journal of Information and Management Sciences

33卷1期（2022 / 03 / 01）

35 - 54

英文

In this paper, the mathematical modeling of generalization of Shannon entropy has been introduced. Thereafter, we proposed an entropy measure for intuitionistic Fuzzy Set and also examine their properties. We have incorporated a term that is Correlation coefficient and using this term Extended VIKOR (Vlsekriterijumska OPtimizacija i KOmpromisno Resenje) method is employed for determining the best alternative instead of distance measure. Thus, the key innovation is to combine the traditional VIKOR model with intuitionistic fuzzy set based on correlation coefficient method. Further, criteria weight is to be determined for partially known and unknown cases using Extended Vikor model. To implement the application of proposed entropy in MCDM (Multi-criteria Decision Making) problems we have taken numerical example of supplier selection. Moreover, we have obtained the ranking sequence using Extended Vikor method. In addition, we have also provided sensitive analysis for different values of weight to show the reliability of proposed measure. Finally, comparison has been made with different entropy measures to show the compatibility of proposed measure with existing one.

1. Joshi, R.,Kumar, S.(2019).A new approach in multiple attribute decision making using exponential hesitant fuzzy entropy.International Journal of Information and Management Sciences,30(4),305-322.
   連結：
2. Joshi, R.,Kumar, S.(2016).A new approach in multiple attribute decision making using R-norm entropy and Hamming distance measure.International Journal of Information and Management Sciences,27(3),253-268.
   連結：
3. Joshi, R.,Kumar, S.(2017).Application of interval-valued intuitionistic fuzzy-norm entropy in multiple attribute decision making.International Journal of Information and Management Sciences,28(3),233-251.
   連結：
4. Vikas, A.,Kumar, S.(2020).Fuzzy entropy measures with an applications in decision making under bipolar fuzzy environment based on topsis method.International Journal of Information and Management Sciences,31,99-121.
   連結：
5. Aczel, J.,Darcozy, Z.(1975).On Measures of Information and Their Characterization.New York:Academic Press.
6. Afful-Dadzie, Eric(2014).Fuzzy VIKOR approach: Evaluating quality of internet health information.2014 Federated Conference on Computer Science and Information Systems
7. Atanassov, K. T.(1986).Intuitionistic fuzzy Sets.Fuzzy Sets Syst,20,87-96.
8. Benayoun, R.,Roy, B.,Sussman, B.(1966).ELECTRE Une methode pour guider le choix en presence de points de vue multiples.Note de travail,49
9. Bhandari, D.,Pal, N. R.(1975).Some new information measures for fuzzy sets.Inf. Sci.,67,209-228.
10. Boran, F. E.,Genc, S.,Akay, D.(2011).Personal selection based on intuitionistic fuzzy sets.Hum. Factors Ergon. Manuf. Serv. Ind.,21,493-503.
11. Boran, F. E.,Genc, S.,Kurt, M.,Akay, D.(2009).A multicriteria intuitionistic fuzzy group decision making for supplier selection with Topsis method.Exp. Syst. Appl.,36(8),11363-11368.
12. Brans, J. P.,Mareschel, V.(1984).Promethee: A new family of outranking methods in multicriteria analysis.Operational Research,84,477-490.
13. Chen, T.,Li, C.(2010).Determining objective weights with intuitionistic fuzzy entropy measures: a Comparative analysis.Inf. Sci.,180,4207-4222.
14. De Luca, A.,Termini, S.(1972).A definition of non-probabilistic entropy in the setting of fuzzy set theory.Inf. Control,20,301-312.
15. Devadoss, A. Victor(2017).A Hybrid Scenario FCM with VIKOR Technique for Ranking the factors.Int. J. Pure Appl. Math,119(9),233-244.
16. Divsalar, Mehdi(2017).Extension of the VIKOR method for group decision making with extentded hesitant fuzzy linguistic information.Neural Computing and Applications,30,3589-3602.
17. Gao, M. M.,Sun, T.,Zhu, J. J.(2014).Revised axiomatic definition and structural formula of intuitionistic fuzzy entropy.Control. Decis.,29(3),470-474.
18. Gerstenkorn, T.,Manko, J.(1991).Correlation of intuitionistic fuzzy sets.Fuzzy Sets Syst,44,39-43.
19. Guo, K. H.,Song, Q.(2014).On the entropy for Atanassov’s intuitionistic fuzzy Sets: an interpretation from the perspective of amount of knowledge.Appl. Soft. Comput.,24,328-340.
20. Hung, W. L.,Yang, M. S.(2006).Fuzzy entropy on intuitionistic fuzzy sets.Int. J. Intell. Syst.,21(4),443-451.
21. Hwang, C. L.,Yoon, K.(1981).Multiple Attribute Decision Making.Berlin:Springer-Verlag.
22. Joshi, R.,Kumar, S.(2018).A novel fuzzy decision making method using entropy weights based correlation coefficients under intuitionistic fuzzy environment.International Journal of Fuzzy Systems
23. Joshi, R.,Kumar, S.(2018).A new parametric intuitionistic fuzzy entropy and its application in multiple attribute decision making.Int. J. Appl. Compute. Math.,4(1),52.
24. Li, H.-C.,You, J.-X.,You, X.-Y.,Shan, M.-M.(2015).A novel approach for failure mode and effects analysis using combination weighting and fuzzy VIKOR method.Appl. Soft Comput.,28,579-588.
25. Lin, L.,Yuan, X. H.,Xia, Z. Q.(2007).Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets.J Comp. Syst. Sci.,73(1),84-88.
26. Liu, H. W.,Wang, G. J.(2007).Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets.Euro. J. Operat. Res.,179(1),220-233.
27. Liu, M. F.,Ren, H. P.(2015).A study of multi-attribute decision making based on a new intuitionistic fuzzy entropy measure.Syst. Eng. Theor. Pract.,35(11),2909-2916.
28. Luo, Xiao,Wang, Xuanzi(2017).Extended VIKOR method for intuitionistic fuzzy multiattribute decision-making based on a new distance measure.Hindawi, Mathematical problems in Engineering,article ID 4072486.
29. Mao, J. J.,Yao, D. B.,Wang, C. C.(2013).A novel cross entropy and entropy measures of IFSs and their applications.Knowl. Based Syst.,48,37-45.
30. Mishra, A. R.,Rani, P.,Jain, D.(2017).Information measures based topsis method for multi criteria decision making problem in intuitionistic fuzzy environment.Iran. J. Fuzz. Syst.,14(6),41-63.
31. Opricovic, S.(1998).University of Belgrade.
32. Opricovic, S.,Tzeng, G. H.(2007).Extended VIKOR method in comparison with outranking methods.European Journal of Operational Research,178,514-529.
33. Radhika, S.,Sammeer Kumar, D.(2017).VIKOR method for multicriteria decision making in Academic staff selection.Journal of production Research and management,3(2)
34. Renyi, A.(1961).On measures of entropy and information.Proceeding of 4th Barkley Symposium on Mathematical Statistics and probability
35. Shannon, C. E. (1948). A mathematical theory of communication, Bell Syst. Tech. J., Vol.27, 379-423.
36. Szmidt, E.,Kacprzyk, J.(2002).Using intuitionistic fuzzy sets in group decision-making.Control Cybern,31,1037-1054.
37. Verma, R. K.,Sharma, B. D.(2014).On intuitionistic fuzzy entropy of order-α.Adv. Fuzzy Syst.,Article ID 789890.
38. Vlachos, I. K.,Sergiadis, G. D.(2007).Intuitionistic fuzzy information- application to pattern recognition.Pattern Recognit. Lett.,28,197-206.
39. Wang, J.,Wang, P.(2012).Intuitionistic linguistic fuzzy multi criteria decision-Making method based on intuitionistic fuzzy entropy.Control Decis.,27,1694-1698.
40. Xia, M.,Xu, Z. S.(2012).Entropy/Cross entropy based group decision making under intuitionistic fuzzy environment.Inf. Fusion,13,31-47.
41. Xiong, S. H.,Wu, S.,Chen, Z. S.,Li, Y. L.(2017).Generalized intuitionistic fuzzy entropy and its application in weight determination.Control Decis.,329(5),845-854.
42. Xu, Z. S.(2007).Intuitionistic fuzzy aggregation operators.IEEE Trans. Fuzzy Systs.,15,1179-1187.
43. Xu, Z. S.,Hu, H.(2010).Projection models for intuitionistic fuzzy multiple attribute decision making.Int. J. Inf. Technol. Decis. Mak.,9,267-280.
44. Xu, Z. S.,Yager, R. R.(2006).Some geometric aggregation operators based on intuitionistic fuzzy sets.Int. J. gen. Syst.,35,417-433.
45. Ye, J.(2010).Fuzzy decision making method based on the weighted correlation coefficient under intuitionistic fuzzy environment.European Journal of Operational Research,205,202-204.
46. Zadeh, L. A.(1965).Fuzzy sets.Information and Computation,8(3),338-353.
47. Zadeh, L. A.(1975).The concept of linguistic variable and its application to approximate reasoning.I. Inf. Sci.,8,199-249.
48. Zadeh, L. A.(1968).Probability measures of fuzzy events.J. Math. Anal. Appl.,23,421-427.
49. Zhu, Y. J.,Li, D. F.(2016).A new definition and formula of entropy for intuitionistic fuzzy sets.J. Intell. Fuzzy. Syst.,30(6),3057-3066.