The likelihood-based optimization ordering model for multiple criteria group decision making with Pythagorean fuzzy uncertainty

The purpose of this paper is to propose a useful likelihood measure for determining scalar function order relations and developing a novel likelihood-based optimization ordering model for solving multiple criteria group decision making (MCGDM) problems based on Pythagorean fuzzy (PF) sets. This paper scrutinizes PF order relations based on scalar functions to compare sophisticated uncertain information and establish a precedence order. By way of scalar function order relations, this paper utilizes scalar functions that are associated with Pythagorean membership grades and admissible upper approximations to present a novel likelihood measure in PF contexts. With the aid of useful concepts, such as levels of agreement and disagreement and comprehensive performance values, this paper originates a PF likelihood-based optimization ordering model to acquire the optimal group consensus solution for addressing MCGDM problems. Practical applications and several comparative studies are performed to reveal the practicality and strong points of the proposed methodology in tackling real-world MCGDM issues within uncertain environments of PF sets. This paper finds that the new scalar function-based likelihood measure is more flexible and beneficial than the current probability distribution approach. Furthermore, an easy-to-use algorithmic procedure can realize the proposed methodology to efficaciously process sophisticated PF information and improve the understandability of a decision model via a likelihood comparison approach. The originality and main contributions of this work are fourfold: (1) A PF likelihood measure is introduced as a basis for scalar function order relations; (2) the PF likelihood-based optimization ordering model is established for consensus ranking; (3) a predominant procedure is constructed for addressing PF information; and (4) the likelihood-based decision models are enriched under complex uncertainty.