A Novel Approach to Reducing Matrix Size in a Fuzzy Setting: The Mean Ranking Method for Solving Traveling Salesman Problems

Abstract

With all inputs being fuzzy numbers, this study proposes an improved matrix reduction method to solve the fuzzy transportation
issue. Fuzzy trapezoidal numbers are transformed into crisp sets utilizing Mean approaches, and the provided solution
for the fuzzy transportation issue is used, as ranking fuzzy numbers is a useful tool for decision making. Along with comparing
the ideal value to various methods, we provide a numerical example that is appropriate for imbalanced. Based on the results,
the suggested strategy under the robust ranking method outperforms the other way when it comes to the optimal profit of
transportation problems. Interesting novel approach to transportation issue management based on fuzzy algorithms is shown
in the numerical illustration.