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Pythagorean Fuzzy Partitioned Geometric Bonferroni Mean and Its Application to Multi-criteria Group Decision Making with Grey Relational Analysis

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Abstract

Based on the partitioned structure of the set of criteria, partitioned geometric Bonferroni mean (PGBM) availably takes into account the heterogeneous relationships between the criteria in the information aggregation of multi-criteria decision making, which can describe the internal relationship and external relationship pattern among criteria. Inspired by the idea, we introduce PGBM into the Pythagorean fuzzy environment and propose two new aggregation operators, i.e., Pythagorean fuzzy partitioned geometric Bonferroni mean and weighted Pythagorean fuzzy partitioned geometric Bonferroni mean (WPFPGBM). Meanwhile, we also examine some special cases and properties of these operators. Then, we deeply investigate the application of WPFPGBM in the Pythagorean fuzzy multi-criteria group decision-making (PFMCGDM) problem. Firstly, we employ theWPFPGBM operator to integrate the Pythagorean fuzzy information for each decision maker. Furthermore, with the help of the grey relational analysis, we design an optimization model to determine the weights of the decision makers and further propose a method for the application of PFMCGDM, i.e., obtain the relative relational degree of the alternatives and rank them accordingly. Finally, the assessment of commercial banks’ credit risk in Ghana is used to illustrate and verify our proposed method.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (Nos. 71401026, 71432003, 71571148, 61773352), the Fundamental Research Funds for the Central Universities of China (No. ZYGX2014J100) and the Social Science Planning Project of the Sichuan Province (No. SC15C009).

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Authors and Affiliations

  1. School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Decui Liang & Adjei Peter Darko

  2. Center for West African Studies, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Decui Liang & Adjei Peter Darko

  3. Business School, Sichuan University, Chengdu, 610065, Sichuan, China

    Zeshui Xu

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  1. Decui Liang
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  2. Adjei Peter Darko
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  3. Zeshui Xu
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Correspondence to Zeshui Xu.

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Liang, D., Darko, A.P. & Xu, Z. Pythagorean Fuzzy Partitioned Geometric Bonferroni Mean and Its Application to Multi-criteria Group Decision Making with Grey Relational Analysis. Int. J. Fuzzy Syst. 21, 115–128 (2019). https://doi.org/10.1007/s40815-018-0544-x

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