Application of Interval-valued Intuitionistic Fuzzy R-norm Entropy in Multiple Attribute Decision Making

10.6186/IJIMS.2017.28.3.4

Rajesh Joshi；Satish Kumar

Intuitionistic fuzzy entropy ； IVIFS ； IVIF R-norm entropy ； similarity measure ； MADM ； TOPSIS

International Journal of Information and Management Sciences

28卷3期（2017 / 09 / 01）

233 - 251

英文

The theory of interval-valued intuitionistic fuzzy sets (IVIFSs) is well suitable to deal with the vagueness and hesitancy. In the present communication, we have considered an interval-valued intuitionistic fuzzy (IVIF) R-norm entropy with both uncertainty and hesitancy degrees expressed in terms of IVIFS. Using this IVIF R-norm entropy, we have solved a multiple attribute decision making (MADM) problem in which attribute values are ex- pressed as IVIFSs. In MADM problem, we mainly encounter with two types of problems. First is when we don’t have any information regarding attribute weights and second is when we have little information about attribute weights, i.e., they are partially known to us. In this paper, we have considered both the cases with examples. For the first case, we have used an extension of entropy weight method to calculate the attribute weights and in second case attribute weights are calculated by using the minimum entropy principle method which is based on solving a linear programming model. The two methods are effectively explained by taking real life examples.

1. Joshi, Rajesh,Kumar, Satish(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：
2. Atanassov, K.,Gargov. G.(1989).Interval valued intuitionistic fuzzy sets.Fuzzy sets and systems,31(3),343-349.
3. Atanassov, K.T.(1986).Intuitionistic fuzzy sets.Fuzzy Sets Syst.,20,87-96.
4. Boran, F.,Genc, S.,Kurt, M.,Akay, D.(2009).A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method.Expert systems with applications,36(8),11363-11368.
5. Burillo, P.,Bustince, H.(2001).Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets.Fuzzy Sets Syst.,118,305-316.
6. Chen, S.,Tan, J.(1994).Handling multicriteria fuzzy decision-making problems based vague set theory.Fuzzy Sets Syst.,67,163-172.
7. Chen, T.,Li. C.(2010).Determining objective weights with intuitionistic fuzzy entropy measures: A comparative analysis.Information sciences,180(21),4207-4222.
8. Choo, E.U.,Wedley, W.C.(1985).Optimal criterion weights in repetitive multicriteria decision making.J. Oper. Res. Soc.,36,983-992.
9. Chu, A. T. W.,Kalaba, R.E.,Spingarn, K.(1979).A comparison of two methods for determining the weights of belonging to fuzzy sets.J. Optimiz. Theor. App.,27,531-538.
10. Cornelis, C.,Deschrijver, G.,Kerre, E.(2004).Implication in intuitionistic fuzzy and intervalvalued fuzzy set theory: construction, classification, application.International journal of approximate reasoning,35(1),55-95.
11. De Luca, A.,Termini, S.(1972).A definition of non-probabilistic entropy in the setting of fuzzy set theory.Inf. Control.,20,301-312.
12. Fan, Z.P.(1996).Shenyang, China,Northeastern university.
13. Hung, W.(2003).A note on entropy of intuitionistic fuzzy sets.International journal of uncertainty, fuzziness and knowledge based systems,11(5),627-633.
14. Hwang, C.L.,Lin, M.J.(1987).Group decision making under multiple criteria: methods and applications.Berlin, Germany:Springer.
15. Joshi, Rajesh,Kumar, Satish(2017).A new exponential fuzzy entropy of order (α , β) and its application in multiple attribute decision-making problems.Communication in mathematics and statistics,5,213-229.
16. Joshi, Rajesh,Kumar, Satish(2017).Parametric (R, S)-norm entropy on intuitionistic fuzzy sets with a new approach in multiple attribute decision making.Fuzzy information and engineering,9,181-203.
17. Joshi, Rajesh,Kumar, Satish(2017).A new intuitionistic fuzzy entropy of order- with applications inmultiple attribute decision making.Proceedings of 6th international conference on soft computing for problem solving, Advances in intelligent systems and computing
18. Joshi, Rajesh,Kumar, Satish,Manocha, Amit(2017).An R-norm fuzzy entropy of type α on intuitionistic fuzzy sets and its applications in multiple attribute decision making.International conference on communication and computing systems, CRC Press,London:
19. Kaufman, A.(1975).Introduction to the theory of fuzzy subsets.New York:Academic press.
20. Kim, S. H.,Choi, S. H.,Kim, I. K.(1999).An interactive procedure for multiple attribute group decision making with incomplete information: range based approach.European Journal of Operational Research,118,139-152.
21. Li, D.(2005).Multiattribute decision-making models and methods using intuitionistic fuzzy sets.J. Comput. Syst. Sci.,70,73-85.
22. Li, D.(2010).TOPSIS-based nonlinear-programming methodology for multi-attribute decision making with interval valued intuitionistic fuzzy sets.IEEE transactions on fuzzy systems,18(2),299-311.
23. Saaty, T. L.(1980).The analytical hierarchy process.New York, NY, USA.:McGraw-Hill.
24. Szmidt, E.,Kacprzyk, J.(2001).Entropy for intuitionistic fuzzy sets.Fuzzy Sets and Systems,118(3),467-477.
25. Vlachos, I.K.,Sergiadis, G.D.(2007).Intuitionistic fuzzy information-applications to pattern recognition.Pattern Recognition Letters,28(2),197-206.
26. Wang, J.,Wang, P.(2012).Intuitionistic linguistic fuzzy multi-criteria decision-making method based on intuitionistic fuzzy entropy.Control. Decis.,27,1694-1698.
27. Wu, J.,Zhang, Q.(2011).Multicriteria decision-making method based on intuitionistic fuzzy weighted entropy.Expert Syst. Appl.,38,916-922.
28. Xu, Z.(2008).Intuitionistic fuzzy information aggregation: theory and application.Beijing:Science press.
29. Xu, Z.(2007).Multi-person multi-attribute decision-making models under intuitionistic fuzzy environment.Fuzzy Optimization and Decision Making,6,221-236.
30. Yager, A.(1982).On measures of fuzziness and fuzzy complements.International journal of general systems,8(3),169-180.
31. Yager, R.(2000).Fuzzy modeling for intelligent decision making under uncertainty.IEEE transactions on systems, man and cybernatics, Part B: Cybernatics,30(1),60-70.
32. Yao, J.,Dash, M. Tan,Liu. H(2000).Entropy-based fuzzy clustering and fuzzy modeling.Fuzzy sets and systems,113(3),381-388.
33. Ye, J.(2010).Multicriteria fuzzy decision making methods using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets.Applied mathematical modeling,34(12),3864-3870.
34. Zadeh L.(2008).Is there a need for fuzzy logic?.Information sciences,178(13),2751-2779.
35. Zadeh, L.A.(1968).Probability measures of fuzzy events.J. Math. Anal. Appl.,23,421-427.
36. Zadeh, L.A.(1965).Fuzzy sets.Information and control,8(3),338-353.
37. Zeng, W.,Yu. F.,Yu, X.,Chen, H.,Wu, S.(2009).Entropy on intuitionistic fuzzy set based on similarity measure.International journal of innovative computing, information and control,5(12),4737-4744.
38. Zhang, H.,Zhang, W.,Mei, C.(2009).Entropy on interval-valued fuzzy sets based on distance and its relationship with similarity measure.Knowledge-based systems,22(6),449-454.
39. Zhang, Q.,Jiang, S.(2008).A note on information entropy measure for vague sets.Inf. Sci.,178,4184-4191.
40. Zhang, Q.,Jiang, S.,Jia, B.,Luo, S.(2010).Some information measures for interval-valued intuitionistic fuzzy sets.Information sciences,180(24),5130-5145.

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