No abstract

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.

a b s t r a c tMolodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft semirings by using the soft set theory. The notions of soft semirings, soft subsemirings, soft ideals, idealistic soft semirings and soft semiring homomorphisms are introduced, and several related properties are investigated.

No abstract

No abstract