Typical hesitant fuzzy rough sets

This paper studies the constructive approach for rough set approximation operators in the typical hesitant fuzzy environment where the typical hesitant fuzzy set (THFS) is a generalization of the classical fuzzy set by possessing a membership degree of a finite non-empty subset of the unitary interval. Firstly, the basic definitions and the existing order structure of the THFSs is reviewed. A new partial order of typical hesitant fuzzy elements (THFEs) is proposed. The intersection and the union of it are further defined and their properties are studied. Secondly, the typical hesitant fuzzy rough approximation operators are constructed based on the aforementioned intersection and union. The representations of both the hesitant fuzzy rough approximation operators and the rough hesitant fuzzy approximation operators are then presented.