Hesitant fuzzy compatible rough set and its application in hesitant fuzzy soft set based decision making.

In this paper, we establish a systematic framework for the study of hesitant fuzzy compatible rough sets by a constructive approach. In the constructive approach, we introduce the concept of lower and upper hesitant fuzzy compatible rough approximation operators and also investigate some properties of this model. Then the concepts of roughness measure and approximate precision of a crisp set in hesitant fuzzy compatible approximation space are proposed and their basic properties are further discussed. Based on the hesitant fuzzy compatible rough sets, a novel decision-making approach to hesitant fuzzy soft sets is established. Meanwhile, a practical example is provided to demonstrate the effectiveness of this method. Finally, by comparing the novel method with the decision making method based on fuzzy soft sets, we point out some advantages of the novel method. [ABSTRACT FROM AUTHOR]