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A parametric likelihood measure with beta distributions for Pythagorean fuzzy decision-making

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Abstract

The objective of this research is to introduce a parametric likelihood measure based on the beta distribution and develop a likelihood-oriented methodology for solving multiple criteria decision analysis (MCDA) problems with Pythagorean fuzzy (PF) sets. With the rapid advancement of PF theory, exploring an effective approach to compare PF information is indispensable in resolving MCDA issues. The beta distribution is one the most commonly used distributions to simulate the theoretical distribution. By changing the parameter values, the beta distribution can generate symmetrical or asymmetrical patterns and various shapes, including flat or steep. Due to its flexibility and adaptability, the beta distribution is able to effectively solve complex real-world problems. To make a major contribution to the technical development of decision support applications, this paper utilizes beta distributions as a parameterization tool to introduce a new parametric likelihood measure for evaluating the outranking relationships among PF information (signified by Pythagorean membership grades). Based on the evolved likelihood-based concepts (e.g., mean outranking indices, weighted outranking grades, and comprehensive outranking measures and indices), this paper proposes a pragmatic PF likelihood-oriented method to prioritize competing alternatives under uncertain and ambiguous Pythagorean fuzzy conditions. To carefully examine the practicality and suitability of the proposed methodology in realistic decision-making environments, this paper utilizes the evolved methods to solve a realistic MCDA problem of selecting pilot hospitals in relation to postacute care. The main results that are generated by the practical application and subsequent experimental analysis and comparative study demonstrate the effectivity and superiority of the developed technique and can be used for practical purposes in flexible and convenient ways. This most important conclusion of this paper is the great aptitude and dominance of the proposed methodology based on the corroboration of the experimental and comparative results of the application. Furthermore, this study has a noticeable originality in the utilization of the generic beta distribution-based approach and the construction of an effective PF likelihood-oriented decision model, which enriches the development of decision-making applications with PF theory.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors acknowledge the assistance of the respected editor and the anonymous referees for their insightful and constructive comments, which helped to improve the overall quality of the paper. The first author is grateful for grant funding support from Chang Gung Memorial Hospital, Linkou, Taiwan (BMRP 864). The corresponding author is grateful for grant funding support from the Ministry of Science and Technology, Taiwan (MOST 110-2410-H-182-005), and Chang Gung Memorial Hospital, Linkou, Taiwan (BMRP 574), during the completion of this study.

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  1. Department of Industrial and Business Management, Graduate Institute of Management, Chang Gung University, No. 259, Wenhua 1st Rd., Guishan District, Taoyuan City, 33302, Taiwan

    Chueh-Yung Tsao & Ting-Yu Chen

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  1. Chueh-Yung Tsao
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  2. Ting-Yu Chen
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Contributions

CYT contributed to methodology, software, validation, formal analysis, writing—original draft, writing—review and editing, and funding acquisition. TYC contributed to conceptualization, methodology, formal analysis, data curation, writing—original draft, visualization, writing—review and editing, and funding acquisition.

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Correspondence to Ting-Yu Chen.

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Tsao, CY., Chen, TY. A parametric likelihood measure with beta distributions for Pythagorean fuzzy decision-making. Neural Comput & Applic 34, 13757–13806 (2022). https://doi.org/10.1007/s00521-022-07151-2

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