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On Characterization of Fuzzy Soft Rough Sets Based on a Pair of Border Implicators

Gong Z., Zhang X.

Fundamenta Informaticae

2015

Vol. 137, nr 4

457--491

Fuzzy set theory, soft set theory and rough set theory are powerfulmathematical tools for dealing with various types of uncertainty. This paper is devoted to define a broad family of soft fuzzy rough sets, each one of which, called an (I, J)-soft fuzzy rough set, is determined by a pair of border implicators (I, J). Alternatively, it shows that a fuzzy soft set can induce a T -equivalence fuzzy relation which is used to granulate the universe. In particular, we prove that (I, J)-fuzzy soft rough sets in our work are equivalent to (I, J)-fuzzy rough sets of Yao et al. by using a T -equivalence fuzzy relation determined by a fuzzy soft set. Furthermore, basic properties of (I, J)-fuzzy soft rough sets are investigated. Meanwhile, an operator-oriented characterization of (I, J)-fuzzy soft rough sets is proposed. Finally, an example is given to illustrate the approach of present paper.