Soft expert approach in rough fuzzy set and its application in MCDM problem
Abstract
One of the interesting parts in the study of uncertainty is to learn about their fusion models. In particular, while studying about fuzzy set and rough set, one may be interested to know about their joint models. Rough fuzzy sets and fuzzy rough sets are those types. After the introduction of soft sets, many research developments started emerging both in the theoretical and application prospective manner. Though this theory sounds good, it has its own limitation in describing expert opinion. To overcome this difficulty the novel idea of soft expert set was being developed. This paper attempts to inter-relate soft expert set with rough fuzzy set in theoretical aspect. An approach to decision-making situation based on the soft expert rough fuzzy set model is also given in a lucid manner..
Keywords:
Fuzzy set , SE set, SEA-space, SER-approximationsReferences
- [1] H. Aktaş & N. Çağman, Soft sets and soft groups, Information Sciences, 177(13) (2007), 2726–2735, DOI:
- [2] https://doi.org/10.1016/j.ins.2006.12.008.
- [3] S. Alkhazaleh & A. R. Salleh, Soft expert sets, Advances in Decision Sciences, 2011 (2011), 757868, DOI:
- [4] https://doi.org/10.1155/2011/757868.
- [5] S. Alkhazaleh & A. R. Salleh, Fuzzy soft expert set and its application, Applied Mathematics, 5 (2014), 1349–1368, DOI: DOI:
- [6] 4236/am.2014.59127.
- [7] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87–96, DOI: https://doi.org/10.1016/S0165-
- [8] (86)80034-3.
- [9] D. Dubois & H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems, 17(2-3) (1990),
- [10] –209, DOI: https://doi.org/10.1080/03081079008935107.
- [11] F. Feng, Y.B. Jun, X. Liu & L. Li, An adjustable approach to fuzzy soft set based decision making, Journal of Computational
- [12] and Applied Mathematics, 234(1) (2010), 10–20, DOI: https://doi.org/10.1016/j.cam.2009.11.055.
- [13] F. Feng, C. Li, B. Davvaz & M.I. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing,
- [14] (9) (2010), 899-911, DOI: https://doi.org/10.1007/s00500-009-0465-6.
- [15] M.B. Gorzalczany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems,
- [16] (1) (1987), 1–17, DOI: https://doi.org/10.1016/0165-0114(87)90148-5.
- [17] Y. Jiang, Y. Tang & Q. Chen, An adjustable approach to intuitionistic fuzzy soft sets based decision making, Applied
- [18] Mathematical Modelling, 35(2) (2011), 824–836, DOI: https://doi.org/10.1016/j.apm.2010.07.038
- [19] S. Kalaiselvan & S. Vijayabalaji, Soft expert symmetric group and its application in MCDM problem, Symmetry, 14(12) (2022),
- [20] , DOI: https://doi.org/10.3390/sym14122685.
- [21] P. Majumdar & S.K. Samanta, Generalised fuzzy soft sets, Computers and Mathematics with Applications, 59(4) (2010),
- [22] -1432, DOI: https://doi.org/10.1016/j.camwa.2009.12.006.
- [23] D. Meng, X. Zhang & K. Qin, Soft rough fuzzy sets and soft fuzzy rough sets, Computers and Mathematics with Applications,
- [24] (12) (2011), 4635-4645, DOI: https://doi.org/10.1016/j.camwa.2011.10.049.
- [25] D. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37(4-5) (1999), 19–31, DOI:
- [26] https://doi.org/10.1016/S0898-1221(99)00056-5.
- [27] J.N. Mordeson, K.R. Bhutani & A. Rosenfeld, Fuzzy group theory, Springer-Verlag Berlin Heidelberg, 2005.
- [28] Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11(5) (1982), 341–356, DOI:
- [29] https://doi.org/10.1007/BF01001956.
- [30] Z. Pawlak, Rough sets: Theoretical aspects of reasoning about data, Kluwer Academic Publishers, 1991.
- [31] Z. Pawlak & R. Sowinski, Rough set approach to multi-attribute decision analysis, European Journal of Operational Research,
- [32] (3) (1994), 443–459, DOI: https://doi.org/10.1016/0377-2217(94)90415-4.
- [33] A. Sezgin & A.O. Atagün, On operations of soft sets, Computers and Mathematics with Applications, 61 (2011), 1457-1467,
- [34] DOI: https://doi.org/10.1016/j.camwa.2011.01.018.
- [35] B. Sun & W. Ma, Soft fuzzy rough sets and its application in decision making, Artificial Intelligence Review, 41(1) (2014),
- [36] -80, DOI: https://doi.org/10.1007/s10462-011-9298-7.
- [37] S. Vijayabalaji, S. Kalaiselvan, N. Thillaigovindan & B. Davvaz, Modified soft-rough modules and their approximations, Journal
- [38] of Multiple-Valued Logic and Soft Computing, 41(6) (2023), 509–535.
- [39] G. Xiao, D. Xiang & J. Zhan, Fuzzy soft modules, East Asian Mathematical Journal, 28(1) (2012), 1–11.
- [40] X.B. Yang, T.Y. Lin, J.Y. Yang, Y. Li & D.J. Yu, Combination of interval-valued fuzzy set and soft set, Computers and
- [41] Mathematics with Applications, 58(3) (2009), 521–527, DOI: https://doi.org/10.1016/j.camwa.2009.04.019.
- [42] L.A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338–353, DOI: https://doi.org/10.1016/S0019-9958(65)90241-X.
- [43] H. Zhang, L. Shu & S. Liao, Intuitionistic fuzzy soft rough set and its application in decision making, Abstract and Applied
- [44] Analysis, 2014 (2014), 287314, DOI: https://doi.org/10.1155/2014/287314.
- [45] X. Zhang & F. Zhu, Rough logic system RSL and fuzzy logic system Luk, Journal of the University of Electron Science and
- [46] Technology of China, 40(2) (2011), 296–302.
- [47] K.Y. Zhu & B.Q. Hu, A new study on soft rough fuzzy lattices (ideals, filters) over lattices, Journal of Intelligent and Fuzzy
- [48] Systems, 33(4) (2017), 2391–2402, DOI: 10.3233/JIFS-17520.