Rough approximate operators based on fuzzy soft relation

Abstract

Fuzzy soft set is a mapping from a parameter set to the collection of fuzzy subset of universal set.  In this paper fuzzy soft relation is presented based on the cartesian product of fuzzy soft sets and the notion of fuzzy soft equivalence relation is introduced.  We prove that every fuzzy soft equivalence relation on an arbitrary fuzzy soft set partition the given fuzzy soft set into equivalence classes and thus induces a new relation on the parameter set.  Basic properties of the induced relation are studied.  A pair of rough approximate operators are investigated and their related properties are given.  Relationship between a fuzzy soft topological space and rough approximate operators based on fuzzy soft relation is further established.