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

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.