On Typical Hesitant Fuzzy Prioritized “or” Operator in Multi-Attribute Decision Making

Abstract

Since hesitant fuzzy set was proposed, multi‐attribute decision making (MADM) with hesitant fuzzy information, which is also called hesitant fuzzy MADM, has been a hot research topic in decision theory. This paper investigates a special kind of hesitant fuzzy MADM problems in which the decision data are expressed by several possible values, and the evaluative attributes are in different priority levels. Firstly, we introduce the definitions of hesitant fuzzy t‐norm and t‐conorm by extending the notions of t‐norm and t‐conorm to the hesitant fuzzy environment and explore their constructions by means of t‐norms and t‐conorms. Then motivated by the prioritized “or” operator (R. R. Yager, Prioritized aggregation operators, International Journal of Approximate Reasoning 2008;48:263–274), we develop the typical hesitant fuzzy prioritized “or” operator based on the developed hesitant fuzzy t‐norms and t‐conorms. In this operator, the degree of satisfaction of each alternative in each priority level is derived from a hesitant fuzzy t‐conorm to preserve trade‐offs among the attributes in the same priority level, and the priority weights of attributes are induced by a hesitant fuzzy t‐norm to model the prioritization relationship among attributes. Furthermore, we apply the developed typical hesitant fuzzy prioritized “or” operator to solving the MADM problems in which the decision data are expressed by several possible values and the attributes are in different priority levels. In addition, two numerical examples are given to, respectively, illustrate the applicability and superiority of the developed aggregation operator by comparative analyses with previous research.

Typical Hesitant Fuzzy Sets: Evaluating Strategies in GDM Applying Consensus Measures

“…Since then, they have been studied, exploring the properties of hesitant fuzzy connectives, providing examples and investigating extensions from other fuzzy logic approaches. Then, some works came next, such as [5], [4], [30], [14], [20], [25] [43] and [40].…”

Hesitant Fuzzy Variable and Distribution

“…Zhang et al established some consistency models in order to obtain missing elements for incomplete hesitant fuzzy preference relations. In addition, some aggregation operators have been introduced to fuse hesitant fuzzy sets in decision making [12][13][14][15][16]. These operators are able to provide powerful guarantees for decision makers to handle complex situations.…”

Integrations of Continuous Hesitant Fuzzy Information in Group Decision Making With a Case Study of Water Resources Emergency Management

“…Existing calculation and integration methods for hesitant fuzzy information are mainly derived from the work of Xia and Xu [7]. After that research, several hesitant fuzzy information aggregation methods [8][9][10][11][12] have been proposed one after another. Subsequently, with the introduction of probabilistic hesitant fuzzy set (P-HFS) and probabilistic linguistic term set (PLTS), some researches [13][14][15][16][17][18][19] on their integration methods also appeared.…”