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Deviation Degree: A Perspective on Score Functions in Hesitant Fuzzy Sets

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Abstract

Score functions play an important role in ranking hesitant fuzzy elements (HFEs) and hesitant fuzzy sets (HFSs). Currently, various kinds of HFE and HFS score functions have been investigated in the literature. However, the essential characteristic and generation mechanism of these score functions have not been systematically studied. To address these issues, this paper introduces an axiomatic definition of deviation degree measure and proposes a general form of dual HFE and HFS deviation score functions, from which a family of existing HFE and HFS score functions can be derived. Besides, we develop two ranking methods based on a pair of dual deviation score functions for distinguishing HFEs and HFSs that are indiscernible by a single score function. Moreover, the mathematical and behavioral properties of HFS deviation score functions are analyzed for applying them in practice. Finally, the proposed ranking method for HFSs is applied to the multi-criteria decision-making problems with hesitant fuzzy information.

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Acknowledgements

The authors are very grateful to the respectful Editors and the anonymous referees for their insightful and constructive comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 61703363, 61876103), the Shanxi Provincial Youth Science and Technology Foundation (Grant No. 201701D221098), the Applied Basic Research Program of Shanxi Province (Grant No. 201801D121148), the Open Project Foundation of Intelligent Information Processing Key Laboratory of Shanxi Province (Grant No. CICIP2018008), and the Doctor Scientific Research Fund Project of Yuncheng University (Grant No. YQ-2016006).

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Authors and Affiliations

  1. School of Mathematics and Information Technology, Yuncheng University, Yuncheng, 044000, Shanxi, China

    Baoli Wang

  2. Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information Technology, Shanxi University, Taiyuan, 030006, Shanxi, China

    Jiye Liang & Jifang Pang

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  1. Baoli Wang
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  2. Jiye Liang
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  3. Jifang Pang
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Correspondence to Baoli Wang.

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Wang, B., Liang, J. & Pang, J. Deviation Degree: A Perspective on Score Functions in Hesitant Fuzzy Sets. Int. J. Fuzzy Syst. 21, 2299–2317 (2019). https://doi.org/10.1007/s40815-019-00722-x

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  • DOI: https://doi.org/10.1007/s40815-019-00722-x

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