Pythagorean fuzzy transportation problem: New way of ranking for Pythagorean fuzzy sets and mean square approach

The predominant domain for optimization in the current situation is the transportation problem (TP). In the majority of cases, accurate data have been employed, yet in reality, the values are vague and imprecise. In any decision-making process, imprecision is a significant issue. To deal with the ambiguous setting of collective decision-making, many tools and methods have been established. The Pythagorean fuzzy set is an extension of fuzzy sets that successfully handles ambiguity and fuzziness. To overcome the shortcomings of intuitionistic fuzzy context, Pythagorean fuzzy sets are considered to be the most recent tools. This study proposes a new method for addressing the uncertain Pythagorean transportation issue. In this study, we created a novel sorting technique for Pythagorean fuzzy sets that converts uncertain quantities into crisp numbers. We developed an innovative mean square strategy for obtaining the initial basic feasible solution (IBFS) for a Pythagorean Fuzzy Transit Issue (PyFTP) of three types (I, II, III) wherein the requirement, availability, and unit of transportation expenses are all in Pythagorean uncertainty. In addition, we used the MODI technique to find the best option. To demonstrate the suggested strategy, we used numerical problems of three distinct kinds. A comparison table with the results of the previous strategy and the suggested method is created to state the benefits of the ranking methodology with the proposed algorithm. The discussion of future research and conclusions is the final step.