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Zbl 1201.03046
Feng, Feng; Li, Changxing; Davvaz, B.; Ali, M.Irfan
Soft sets combined with fuzzy sets and rough sets: a tentative approach. (English)
[J] Soft Comput. 14, No. 9, 899-911 (2010). ISSN 1432-7643; ISSN 1433-7479/e

Summary: Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Dubois and Prade investigated the problem of combining fuzzy sets with rough sets. Soft set theory was proposed by Molodtsov as a general framework for reasoning about vague concepts. The present paper is devoted to a possible fusion of these distinct but closely related soft computing approaches. Based on a Pawlak approximation space, the approximation of a soft set is proposed to obtain a hybrid model, called rough soft sets. Alternatively, a soft set instead of an equivalence relation can be used to granulate the universe. This leads to a deviation of Pawlak approximation space, called a soft approximation space, in which soft rough approximations and soft rough sets can be introduced accordingly. Furthermore, we also consider approximation of a fuzzy set in a soft approximation space, and initiate a concept called soft-rough fuzzy sets, which extends Dubois and Prade's rough fuzzy sets. Further research will be needed to establish whether the notions put forth in this paper may lead to a fruitful theory.

MSC 2000:: *03E72 Fuzzy sets (logic)
68T37 Reasoning under uncertainty

Keywords: soft set; fuzzy set; rough set; rough fuzzy set; approximation space; approximation operator

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Zentralblatt MATH Berlin [Germany]