Abstract:

A general framework is presented for the study of generalized interval-valued fuzzy rough sets integrating the rough set theory with the interval-valued fuzzy set theory by using constructive approach. Firstly, through employing an interval-valued fuzzy residual implicator and its dual operator, generalized upper and lower interval-valued fuzzy rough approximation operators with respect to an arbitrary interval-valued fuzzy approximation space are first defined. Based on properties of interval-valued fuzzy residual implicator on LI,  some interesting properties of interval-valued fuzzy rough approximation operators are then examined. In the axiomatic approach, interval-valued fuzzy rough approximation operators are further defined by axioms. And different axiom sets can characterize the essential properties of interval-valued fuzzy rough approximation operators.

Key words:  interval-valued fuzzy sets; interval-valued fuzzy relation; interval-valued fuzzy rough approximation operators; axiomatic approach