Optimizing Transportation and Group Decision-Making Problems Using Improved Aggregation Operator and Information Measures in Pythagorean Fuzzy Framework

Pythagorean fuzzy set theory generalizes the notion of intuitionistic fuzzy sets and provides a more efficient tool to handle uncertainty and vagueness in real-world situations. This study explores the advantages of Pythagorean fuzzy set theory in decision-making contexts such as (i) transportation problems and (ii) multi-criteria group decision-making problems with Pythagorean fuzzy information. First, we highlight some shortcomings/limitations in weighted geometric aggregation operators for Pythagorean fuzzy numbers as defined in the literature. A new weighted geometric aggregation operator is proposed using advanced algebraic operational laws in order to overcome the shortcomings of weighted geometric aggregation operators. In addition, novel divergence and entropy measures have been introduced, followed by a discussion of their properties. A new solution technique is also proposed to solve the transportation problem, which has cost coefficients such as Pythagorean fuzzy numbers, employing the proposed aggregation operator and divergence measure. Further, an integrated Entropy–MARCOS approach for solving multi-criteria decision-making problems has been suggested. These solution methodologies are demonstrated with the help of numerical examples. A comparative study is also included to show the efficacy of proposed approaches over existing ones in resolving the issues of considered decision-making. Finally, the significance and conclusions of this study have been presented.