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Multiplicative Consistency Adjustment Model and Data Envelopment Analysis-Driven Decision-Making Process with Probabilistic Hesitant Fuzzy Preference Relations

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Abstract

Unlike other fuzzy modellings, probabilistic fuzzy sets can reflect clearly the importance of different numerical values. In group decision-making (GDM) problems, it is quite common for decision-makers (DMs) to elicit their knowledge with probabilistic hesitant fuzzy preference relations (PHFPRs), in which consistency adjustment and alternatives’ weight vector determination play a key role in the decision-making process. This study aims at constructing a decision-making model with PHFPRs. First, several new concepts are introduced, including the multiplicative consistency and consistency index of PHFPRs. Then, we present a construction approach for the multiplicative consistent PHFPRs, and a convergent local consistency improvement process for PHFPRs is designed to detect and improve their consistency when the PHFPRs do not meet the consistency level. The local adjustment strategy is utilized to retain the preference evaluation of DMs as much as possible. Afterwards, based on the obtained efficiency score values, we propose a new data envelopment analysis model to derive the weight values of alternatives. Furthermore, we explore a decision-making method with PHFPRs to obtain the optimal selection from the alternatives. Finally, an applied case about logistics company assessment is presented, and the effectiveness and rationality of the explored method are verified by the comparison with the various approaches.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Nos. 71901001, 71871001), Natural Science Foundation of Anhui Province (Nos. 2008085MG226, 2008085QG333), the Construction Fund for Scientific Research Conditions of Introducing Talents in Anhui University (No. S020118002/085), the Humanities and Social Sciences Planning Project of the Ministry of Education (No. 20YJAZH066).

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Authors and Affiliations

  1. School of Business, Anhui University, Hefei, 230601, Anhui, China

    Feifei Jin & Jinpei Liu

  2. School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, 147004, Punjab, India

    Harish Garg

  3. School of Mathematics and Statistics, Hefei Normal University, Hefei, 230601, Anhui, China

    Lidan Pei

  4. School of Mathematical Sciences, Anhui University, Hefei, 230601, Anhui, China

    Huayou Chen

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  1. Feifei Jin
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  2. Harish Garg
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  3. Lidan Pei
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  4. Jinpei Liu
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  5. Huayou Chen
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Correspondence to Harish Garg or Jinpei Liu.

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Jin, F., Garg, H., Pei, L. et al. Multiplicative Consistency Adjustment Model and Data Envelopment Analysis-Driven Decision-Making Process with Probabilistic Hesitant Fuzzy Preference Relations. Int. J. Fuzzy Syst. 22, 2319–2332 (2020). https://doi.org/10.1007/s40815-020-00944-4

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  • DOI: https://doi.org/10.1007/s40815-020-00944-4

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