D-Intuitionistic Hesitant Fuzzy Sets and their Application in Multiple Attribute Decision Making

Hesitant fuzzy sets (HFSs) and generalized hesitant fuzzy sets (GHFSs) provide useful tools for uncertain information processing in situations in which decision makers have doubts among several possible membership degrees. In practice, however, decision makers may have a degree of belief for hesitant memberships based on their knowledge and experience. The aim of our study is to propose a new manifestation of uncertain information, called D-intuitionistic hesitant fuzzy sets (D-IHFSs), by combining D numbers and GHFSs. First, arithmetic operations, score functions, and comparison laws related to D-IHFSs are introduced. Next, an extension principle is proposed for the application of aggregation operators of GHFSs to the D-intuitionistic hesitant fuzzy environment. Finally, a decision-making approach based on D-IHFSs is developed. An illustrative example shows the effectiveness and flexibility of D-IHFSs to handle uncertainties, such as fuzziness, hesitation, and incompleteness. D-IHFSs, combining D numbers and GHFSs, improve decision makers' ability to handle uncertain information.