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The normal parameter reduction of soft sets and its algorithm. (English) Zbl 1165.90699

Summary: This paper is concerned with the reduction of soft sets and fuzzy soft sets. Firstly, the problems of suboptimal choice and added parameter set of soft sets are analyzed. Then, we introduce the definition of normal parameter reduction in soft sets to overcome these problems. In addition, a heuristic algorithm of normal parameter reduction is presented. Two new definitions, parameter important degree and decision partition, are proposed for analyzing the algorithm of normal parameter reduction. Furthermore, the normal parameter reduction is also investigated in fuzzy soft sets.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
68T37 Reasoning under uncertainty in the context of artificial intelligence
03E72 Theory of fuzzy sets, etc.
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References:

[1] Zadeh, L. A., Fuzzy sets, Inform. Control, 8, 338-353 (1965) · Zbl 0139.24606
[2] Pawlak, Z., Rough sets, Int. J. Inform. Comput. Sci., 11, 341-356 (1982) · Zbl 0501.68053
[3] Molodtsov, D., The Theory of Soft Sets (2004), URSS Publishers: URSS Publishers Moscow, (in Russian)
[4] Molodtsov, D., Soft set theory-first results, Comput. Math. Appl., 37, 19-31 (1999) · Zbl 0936.03049
[5] Aktas, H.; Cagman, N., Soft sets and soft groups, Inform. Sci., 177, 2726-2735 (2007) · Zbl 1119.03050
[6] Maji, P. K.; Roy, A. R.; Biswas, R., An application of soft sets in a decision making problem, Comput. Math. Appl., 44, 1077-1083 (2002) · Zbl 1044.90042
[7] Maji, P. K.; Bismas, R.; Roy, A. R., Soft set theory, Comput. Math. Appl., 45, 555-562 (2003) · Zbl 1032.03525
[8] Chen, D.; Tsang, E. C.C.; Yeung, D. S.; Wang, X., The parameterization reduction of soft sets and its applications, Computer and Mathematics with Applied, 49, 757-763 (2005) · Zbl 1074.03510
[9] Pawlak, Z., Rough Set: Theoretical Aspects of Reasoning About Data (1991), Kluwer Academic: Kluwer Academic Boston, MA · Zbl 0758.68054
[10] Zimmerman, H. J., Fuzzy Set Theory and its Applications (1996), Kluwer Academic Publishers: Kluwer Academic Publishers Boston
[11] Maji, P. K.; Biswas, R.; Roy, A. R., Fuzzy soft sets, J. Fuzzy Math., 9, 3, 589-602 (2001) · Zbl 0995.03040
[12] Roy, A. R.; Maji, P. K., A fuzzy soft set theoretic approach to decision making problems, Comput. Appl. Math., 203, 412-418 (2007) · Zbl 1128.90536
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