HFGLDS: Hesitant Fuzzy Gained and Lost Dominance Score Method Based on Hesitant Fuzzy Utility Function for Multi-Criteria Decision Making

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Abstract
Hesitant fuzzy set (HFS) is a mighty mathematical tool to represent the hesitant fuzzy information, which can reveal the situation of hesitancy in practical problems. More recently, HFS has been generally utilized in multi-criteria decision-making (MCDM) problem. How to cope with the hesitant fuzzy information effectively is crucial to address the problem of MCDM under hesitant fuzzy environment. In this study, a novel hesitant fuzzy utility function is proposed to depict the hesitant fuzzy information contained in the hesitant fuzzy element (HFE) and realizes the transformation from the hesitant fuzzy information to the crisp value. Firstly, a novel hesitant degree measure is presented to eliminate the drawbacks of traditional methods. The new hesitant degree measure can effectively describe the reliability of the HFE. Afterward, a novel approach of the hesitant fuzzy utility function is constructed by combining the hesitant fuzzy score value and the hesitant degree of the HFE. To generate accurate decision results, we introduce the gained and lost dominance score (GLDS) approach in our work. Then, a new hesitant fuzzy GLDS method is presented based on the GLDS method and the hesitant fuzzy utility function. Furthermore, we utilize the hesitant fuzzy utility value of the alternative to construct the comparison matrix between the criteria, which is used to identify the weight value of the criteria. Ultimately, a practical application is provided to demonstrate the validity and rationality of the proposed method, and comparative analysis with the existing decision making approaches.

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