Applications of probabilistic hesitant fuzzy rough set in decision support system

摘要

The objective of this manuscript is to present the notion of probabilistic hesitant fuzzy rough (PHFR) set and their basic operations. As a generalization of the sets, PHFR set is a more profitable way to express the uncertainties in the data. For it, firstly, we define the basic operational laws like, the union, intersection and the composition of probabilistic hesitant fuzzy approximation spaces with some basic properties are discussed in details. Secondly, presented the novel decision-making technique based on the PHFR sets over two nonempty fixed sets to deal with uncertainty in decision-making problems. Finally, two numerical examples are provided with some comparative study to validate the proposed approach.