Frank Aggregation Operators and Their Application to Probabilistic Hesitant Fuzzy Multiple Attribute Decision-Making

Abstract

The fuzzy aggregation information plays an important role in the group decision support system under the interval-valued hesitant fuzzy information and interval-valued probabilistic hesitant fuzzy information. Therefore, in this paper, we develop a new approach of the interval-valued hesitant fuzzy Frank aggregation (IVHFFA) and interval-valued probabilistic hesitant fuzzy aggregation (IVPHFFA) operators. First, we define some operational laws of IVHEs and IVPHFEs by using Frank t-norm and t-conorm. Furthermore, we develop a series of IVHFFA and IVPHFFA operators based on these operational laws under the IVHF and IVPHF information. Also, discuss some fundamental properties and relations of the proposed aggregation operators for IVHF and IVPHF information. In order to implement the proposed aggregation operators of IVHF and IVPHF information in group decision-making problem, we construct general algorithms for multi-attribute group decision-making problem based on the proposed IVHFFA and IVPHFFA. Finally, from the comparative and sensitivity analysis, the proposed fuzzy decision-making model is more effective and reliable as compared with existing method.