Abstract
Fuzzy set theory, soft set theory and rough set theory are powerful mathematical 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.