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Consensus Building for Probabilistic Hesitant Fuzzy Preference Relations with Expected Additive Consistency

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Abstract

As an extension of hesitant fuzzy element, probabilistic hesitant fuzzy element (PHFE) has received increasing attention. However, some important issues in PHFE utilization remain to be addressed. This study aims to build a consensus among the decision makers for probabilistic hesitant fuzzy preference relations (PHFPRs) with expected additive consistency. First, several generalized operations that are suitable for PHFPRs are defined. Then, expected additive consistent PHFPRs are introduced, and a theorem is proposed to obtain them. Second, the consistency index is defined based on the Hausdorff distance of PHFEs to measure whether individual PHFPRs exhibit acceptable expected additive consistency. If not, then an automatic iterative algorithm is designed to obtain acceptable ones. Third, group PHFPR is obtained based on the proposed generalized operations, and then the consensus index is determined according to the Hausdorff distance. If at least one of the consensus levels of the decision makers is lower than a given threshold, then an automatic iterative algorithm is used to update the PHFPRs to reach a predefined consensus level. Finally, a numerical example is provided, and comparative analyses with existing methods are performed to demonstrate the validity of the proposed method in addressing group decision-making problems.

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Acknowledgement

The authors would like to thank the editors and the anonymous reviewers for their insightful and constructive comments that have led to an improved version of this paper.

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Authors and Affiliations

  1. School of XingJian College of Science and Liberal Arts, Guangxi University, Nanning, 530005, Guangxi, People’s Republic of China

    Jian Li

  2. School of Mathematics and Information Science, Guangxi University, Nanning, 530004, Guangxi, People’s Republic of China

    Zhong-xing Wang

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  1. Jian Li
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Correspondence to Zhong-xing Wang.

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Li, J., Wang, Zx. Consensus Building for Probabilistic Hesitant Fuzzy Preference Relations with Expected Additive Consistency. Int. J. Fuzzy Syst. 20, 1495–1510 (2018). https://doi.org/10.1007/s40815-018-0451-1

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