Multi-attribute Group Decision Making Based on Cloud Aggregation Operators Under Interval-Valued Hesitant Fuzzy Linguistic Environment

Interval-valued hesitant fuzzy linguistic set, as an extension of linguistic term set and interval-valued hesitant fuzzy set, can effectively describe uncertainty, hesitancy, and inconsistency inherent in decision-making process. In this paper, a method based on comprehensive cloud aggregation operators is developed for solving multi-attribute group decision-making (MAGDM) problems with interval-valued hesitant fuzzy linguistic numbers (IVHFLNs). First, a comprehensive cloud of an IVHFLN is defined according to the cloud model. Using the comprehensive cloud, a distance measure between two comprehensive clouds is proposed and a distance measure for comprehensive cloud matrices is developed. Then, some generalized geometric aggregation operators of comprehensive clouds for IVHFLNs are introduced, including a comprehensive cloud generalized weighted geometric operator, a comprehensive cloud generalized ordered weighted geometric operator, and a comprehensive cloud generalized hybrid geometric operator. Subsequently, two approaches are presented to compute the deviations among attributes. Then, a programming model of maximizing deviation is established to derive the attribute weights objectively. To determine DMs’ weights, a technique for order preference by similarity to ideal solution-based approach is put forward in interval-valued hesitant fuzzy linguistic environment. The individual order of alternatives for each decision maker is obtained by the comprehensive cloud aggregation operator. To generate the collective order of alternatives, a multi-objective assignment model is constructed and transformed into a single-objective program to resolve. Thus, a method based on comprehensive cloud aggregation operators is proposed for MAGDM with IVHFLNs. Finally, two examples of application are given to demonstrate the applicability and effectiveness of the proposed method.