Innovative Similarity Distance and Entropy Measures for Interval-Valued Fuzzy Soft Set
Sonia Devi
, Pratiksha Tiwari
, Priti Gupta
Abstract
Interval-valued fuzzy soft sets are one of the most effective methods to deal with uncertainty. In this paper, similarity measures for interval-valued fuzzy soft sets are proposed with their properties and some distance measures are proposed using these measures. The use of proposed similarity measures has been made to define maximin average and convex entropy measures along with the weighted information measures. The application of the proposed similarity and entropy measures is also demonstrated in decision-makingproblem.
References
1. C.P. Wei; P. Wang; Y.Z. Zhang; Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications, Information Sciences, 181(19) 4273– 4286 (2011).
2. D. Molodtsov; Soft set theory—first results, Computers & Mathematics with Applications, 37( 4- 5) 19–31 (1999).
3. De Luca; S. Termini; A definition of a non- probabilistic entropy in the setting of fuzzy sets theory, Information and Control, 20(4)301–312 (1972).
4. J.L. Fan; Y.L. Ma; Some new fuzzy entropy formulas, Fuzzy Sets, and Systems, 128(2) 277–284 (2002).
5. K. Atanassov; Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) 87-96 (1986).
6. K. Atanassov; Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64(2)159.-174 (1994).
7.
8. L.A. Zadeh; Fuzzy sets, Information and Control, 8(3) 338-353 (1965).
9. M. J. Son; Interval-valued fuzzy soft sets, Journal of the Korean Institute of Intelligent Systems, 17(4) 557-562 (2007).
10.M.B. Gorzalzany; A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems, 21(1) 1-17 (1987).
11. Mukhergee; S.Sarkar; Similarity measures of interval-valued fuzzy soft sets and their application in decision making problems, Annals of Fuzzy Mathematics and Informatics, 8(9) 447-460 (2014).
12. Mukherjee; S. Sarkar; Similarity measures for interval-valued intuitionistic fuzzy soft sets and its application in medicaldiagnosis problem, 2(3) 159– 165(2014).
13.N. H. Sulaiman; N. L. A. M. Kamal; (2018) Conference Proceedings Proceeding of the 25th national symposium on mathematical sciences (SKSM25): Mathematical Sciences as the Core of Intellectual Excellence - Pahang, Malaysia (27–29 August 2017)] - A subsethood-based entropy for weight determination in interval-valued fuzzy soft set group decision making, 1974 020062.
14. P. K. Maji; A. R. Roy; R. Biswas; An application of soft sets in a decision making problem, Computers & Mathematics with Applications, 44( 8-9) 1077–1083 (2002).
15.P. K. Maji; R. Biswas; A. R. Roy; Fuzzy soft sets,Journal of Fuzzy Mathematics, 9(3) 589–602 (2001).
16.P. K. Maji; R. Biswas; A. R. Roy; Soft set theory, Computers & Mathematics with Applications,45( 4- 5) 555–562 (2003).
17. P.Yiarayong; On interval valued fuzzy soft set theory applied to semigroupes, Soft Computing, 24(8) 3113-1368(2020).
18. S.Alkhazaleh; A.R.Salleh; Generalised interval valued fuzzy soft set, Journal of Applied Mathematics, vol 2012, Article ID 870504, 18 pages,(2012).
19. S.Alkhazaleh; A.R.Salleh; and N.Hassan, Fuzzy parameterized interval-valued fuzzy soft set, Applied Mathematical Sciences, 5(67), 3335-3346 (2011).
20. S.Alkhazaleh; A.R.Salleh; Soft expert sets, Advances in Decision Sciences. 5(9) 1349-1368 (2011).
21. W. Zeng;H. Li; Inclusion measures, similarity measures, and the fuzziness of fuzzy sets and their relations,International Journal of Intelligent Systems, 21(6) 639–653 (2006).
22.W.J. Wang; New similarity measures on fuzzy sets and on elements, Fuzzy sets and Systems, 85(3) 305- 309 (1997).
23. X. Liu; Entropy, distance measure andsimilarity measure of fuzzy sets and their relations, Fuzzy Sets and Systems, 52(3) 305–318 (1992).
24.X. Peng; H. Garg; Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure, Computer & Industrial Engineering, 119 439-452 (2018).
25.X. Yang; D. Yu; J. Yang; C. Wu; (2007) Generalization of soft set theory: from crisp to fuzzy case, in Proceedings of the 2nd International Conference of Fuzzy Information and Engineering (ICFIE '07), 40 ofAdvances in Soft Computing, 345–354.
26.X.D. Peng; Y. Yang; Information measures for interval-valued fuzzy soft sets and their clustering algorithm, Journal of Computer Applications, 35(8) 2350-2354 (2015)
27.X.D.Peng;J.Dai; H.Y.Yang; Intervalvaluedfuzzy soft decision making methods based on MABAC, similarity measure, and EDAS, FundamentaInformaticae 152(4) 373-396 (2017).
28. X.Yang; T.Y.Lin; J.Yang; Y.Li; and D.Yu; Combination of interval-valued fuzzy set and soft set, Computers, and Mathematics with Applications, 58(3) 521-527 (2009).
29.Y.C. Jiang; Y. Tang; H. Liu; Z.Z. Chen; Entropy on intuitionistic fuzzy soft sets and interval-valued fuzzy soft sets, Information Sciences, 240 95-114 (2013).
30.Y.Zou; Z.Xiao; Data analysis approachesof soft sets underincomplete information, Knowledge-Based System, 21(8) 941-945 (2008).
31.Z. Pawlak; Rough sets; International Journal of Information and Computer Sciences, 11(5) 341-356 (1982).