Representations of typical hesitant fuzzy rough sets

Abstract

Typical hesitant fuzzy set is a kind of generalization of classical fuzzy set by possessing a membership degree, called as typical hesitant fuzzy element, of finite non-empty subset of the unitary interval. This paper studies the constructive approach to rough set approximation operators in typical hesitant fuzzy background. Firstly, two novel partial orders are introduced to compare two arbitrary typical hesitant fuzzy elements and typical hesitant fuzzy sets, meanwhile, the basic operations, including intersection, union and α−level sets of typical hesitant fuzzy sets are then proposed and their properties are studied in detail. Secondly, typical hesitant fuzzy rough sets are introduced and studied via the new operations of intersection and union. Furthermore, typical hesitant fuzzy rough approximation operators are represented by the rough approximation operators of the α−level set of typical hesitant fuzzy set. Finally, the connections between typical hesitant fuzzy (and crisp, respectively) relations and typical hesitant fuzzy rough (and rough typical hesitant fuzzy, respectively) approximation operators are further established.