a theoretical and computational study of a defuzzification function for the generalized fuzzy mtsp

This study presents a parametric approach for solving the single-depot multiple traveling salesman problem (mtsp) in a generalized trapezoidal fuzzy environment. the classical mtsp involves a set of cities and a number of salesmen, all of whom start from and return to a single depot (or home base), with each city required to be visited exactly once by one salesman. our proposed algorithm, specifically designed for the single-depot mtsp, utilizes a two-stage architecture: in the first stage, a defuzzification process is applied to the fuzzy parameters, and in the second stage, the problem is formulated as a mathematical model and solved using matlab 2018. the primary innovation lies in the design of a numerical example alongside the development of related theorems concerning the defuzzification function. furthermore, numerical results from its application to a seven-city problem with fuzzy costs are presented.