Properties of interval-valued hesitant fuzzy sets

Interval-valued hesitant fuzzy sets (IVHFSs), as an extension of hesitant fuzzy sets, can account for the membership degrees of an element to a given set having a few different interval values, which provides an intuitionistic description on the differences among decision makers. We derive the properties and relationships of fundamental operations on IVHFSs for Algebraic t-norm and t-conorm. Furthermore, we present the operations based on Archimedean t-norm and t-conorm and investigate their properties. The results obtained using the two types of t-norms and t-conorms could be useful for applications of IVHFSs in information aggregation and decision making.