On hesitant neutrosophic rough set over two universes and its application

As a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single valued neutrosophic refined set, hesitant fuzzy set, and dual hesitant fuzzy set, Ye (J Intell Syst 24(1):23–36, 2015) proposed the concept of hesitant neutrosophic sets (also called single valued neutrosophic hesitant fuzzy sets). Following the idea of hesitant neutrosophic sets as introduced by Ye, in this paper, the model of hesitant neutrosophic rough sets is proposed, then the join semi-lattice structure of lower and upper hesitant neutrosophic rough approximation operators over two universes is given. In addition, an algorithm to handle decision making problem in medical diagnosis based on hesitant neutrosophic rough sets over two universes is provided. Finally, a numerical example is employed to demonstrate the validness of the proposed hesitant neutrosophic rough sets.