Solution of Transportation Problem Using Interval-Valued Pythagorean Fuzzy Approach

Abstract

In the implementation of real-world problems, there is increased demand on administration to figure out how to get things from point A to point B as cheaply as possible. Transportation problem (TP) models are particularly effective in reducing these difficulties. In a traditional transportation problem, the decision-maker is confident in the product’s transportation cost, availability, and demand. But in a real-life scenario, these variables are uncontrollable due to an imprecision of data. To deal with the ambiguous data and haziness of real-world situations, the concept of a fuzzy set (FS) and its extensions have been defined. It can be difficult to determine the value of membership and non-membership at a given point in some cases. As a result, we have used the membership as well as non-membership values as an interval in the proposed work to find the solution to the transportation problem using an interval-valued Pythagorean fuzzy set (IVPFS). We used the proposed score function (SF) to solve three different types of interval-valued Pythagorean fuzzy transportation problems (IVPFTP) and compared the results with existing score function in the literature. Also we have discussed the algorithm for IVPFTP in the proposed work. Numerical problems for the effectiveness of various types of models are providing to support our work. Finally, we discussed the work's outcome and conclusion.