In this paper, we propose a general framework for the study of dual hesitant fuzzy rough sets integrating rough set theory with dual hesitant fuzzy set theory in which both constructive and axiomatic approaches are considered. In a constructive approach, by using a dual hesitant fuzzy relation, lower and upper dual hesitant fuzzy rough approximation operators with respect to a dual hesitant fuzzy approximation space are first defined and some properties of this model are further discussed. Adopting an axiomatic approach, dual hesitant fuzzy rough approximation operators are defined by axioms. And different axiom sets of dual hesitant fuzzy set-theoretic operators guarantee the existence of different types of dual hesitant fuzzy relations producing the same operators. We then give an approach of decision-making in uncertainty environment by using the dual hesitant fuzzy rough sets. Finally, a practical application in medical diagnosis is provided to illustrate the validity of this approach.
['Haidong Zhang', 'Lan Shu', 'Shilong Liao', 'Cairang Xiawu']
Dual hesitant fuzzy rough set and its application