New Operations over Hesitant Fuzzy Sets

Hesitant fuzzy sets are considered to be the way to characterize vague phenomenon. Their study has opened a new area of research and applications. Set operations on them lead to a number of properties of these sets which are not evident in classical (crisp) sets make the area mathematically also very productive. Since these sets are defined in terms of functions and set of functions, which is not the case when the sets are crisp, it is possible to define several set operations. Such a study enriches the use of these sets. In this paper, four new operations are envisaged, defined and taken up to study a score of new identities on hesitant fuzzy sets.