Generalized hesitant fuzzy rough sets (GHFRS) and their application in risk analysis

As a generalization of fuzzy rough sets, the concept of generalized hesitant fuzzy rough sets (GHFRS) is presented in this paper. It is an endeavor to define rough approximations of a collection of hesitant fuzzy sets over a given universe. To this end, elements of the universe are initially clustered using a set-valued map, and then, hesitant fuzzy sets are aggregated by using lower and upper approximation operators. These operators produce hesitant fuzzy sets which aggregate hesitant fuzzy elements. Structural and topological properties associated with GHFRS have been examined. The model is further employed to design a three-way decision analysis technique which preserves many properties of classical techniques but needs less effort and computation. Unlike the existing approaches, the alternatives can be clustered and selected jointly by using a set-valued mapping. This feature makes its application area broader. Moreover, this method is applied to an example, where risk analysis issue is discussed for the selection of energy projects.