A likelihood-based preference ranking organization method using dual point operators for multiple criteria decision analysis in Pythagorean fuzzy uncertain contexts

Considering the new uncertainty format of Pythagorean fuzzy (PF) sets, this research aims to launch a point operator-based likelihood measure and establish a PF preference ranking organization method for enrichment evaluations (PROMETHEE) to manipulate multiple criteria decision analysis (MCDA) tasks within PF environments. Different from the previous extensions of PROMETHEE into PF circumstances, this research presents dual PF point operators to delineate an innovative likelihood measure as a means to ascertainment of preference relationships. As contrasted with the current probability distribution approach, this research takes advantage of the conception of scalar functions as well as the lower approximated estimations and upper approximated estimations via the dual operators to construct a creative point operator-based likelihood measure. This new likelihood measure has novelty value and possesses several desirable properties, such as boundedness, complementarity, and weak transitivity; thus, it can better reveal the possibility of the dominance relations between PF information. More useful concepts of a likelihood-based predominance index and predominance-based preference functions are proposed to facilitate intra-criteria and inter-criteria comparisons in the forms of PF performance ratings and PF characteristics, respectively. Furthermore, their beneficial and desirable properties are also investigated. On the grounds of these new concepts and measures, a likelihood-based PROMETHEE methodology is exploited to address MCDA problems in uncertain circumstances involving Pythagorean fuzziness. By simultaneously employing the positive and negative predominating flows, the likelihood-based PF PROMETHEE I yields a partial ranking of available alternatives and highlights any possible incomparability between alternatives. Based on the net predominating flow, the likelihood-based PROMETHEE II renders complete ranking orders of alternatives and preclude any incomparability among the competing alternatives. The reasonableness and effectuality of the initiated methodology are demonstrated with the assistance of a realistic case about evaluating financing policies for working capital management and a comparative analysis.