Pythagorean fuzzy likelihood function based on beta distributions and its based dominance ordering model in an uncertain multiple criteria decision support framework

The concept of Pythagorean fuzzy (PF) sets represents a superior tool to model complex uncertainties in an ambiguous and equivocal decision-making framework. In consideration of the significant capacity for exhibiting the uncertainty of subjective appraisals and estimations under the aegis of the PF theory, this paper presents a simple-to-operate decision-making approach that is grounded in some beneficial concepts of original likelihood functions and measurements of dominating and dominated characters. On the strength of beta distributions, this paper seeks to propound new notions of PF likelihood functions and likelihood-oriented dominating/dominated characters and to launch an exploitable multiple criteria evaluation method by means of a dominance ordering model for treating decision analysis within PF environments. This paper initiates an efficient beta distribution-based approach to the construction of novel PF likelihood functions that can quantify the possibility degrees of outranking and outranked relationships between Pythagorean membership grades. The applicable satisfaction and dissatisfaction estimations are established on the likelihood-oriented dominating and dominated characters, respectively. Furthermore, this paper formulates a straightforward dominance ordering model to obtain the ultimate dominance ranking orders of candidate alternatives and accomplish multiple criteria decision-making issues involving complicated uncertainty. A financing decision-making problem concerning working capital requirements is investigated to validate the application results using the advanced methodology. The real-world application is implemented to examine the reasonableness and efficacy of the established techniques. Moreover, comparative studies through the utility of a sensitivity analysis are performed to demonstrate the efficacy and merits of the dominance ordering model. The comparison results manifest that the initiated methodology is an advantageous and reliable decision-making technique that can enhance the methodological development regarding the multiple criteria evaluation model under PF uncertainty. Finally, recommendations for future research directions are also presented in the conclusions.