Fuzzy commercial traveler problem of trapezoidal membership functions within the sort of $$\alpha $$ α optimum solution using ranking technique

Abstract

The commercial traveler problem (CTP) is one of the difficult real—life issues, attracting researchers of the numerous fields together with artificial intelligence, operations research and also algorithm design and analysis. The problems were studied completely on various fields and it has been resolved with different approaches like genetic algorithms and linear programming. Linear programming is intended to take care of crisp parameters, and however data regarding reality world systems is usually offered with in the style of imprecise descriptions. Fuzzy strategies are designed to handle imprecise terms, and are most suited to finding optimum solutions to issues with imprecise parameters. Throughout this paper, solving technique absolutely think about as a CTP with the assistance of trapezoidal membership functions and its arithmetic operations. Solving procedure has been applied from the approach of fuzzy assignment problem using Robust Ranking technique. The fuzzified version of the problem has been mentioned with the assistance of a numerical example associated it is proving that the Robust ranking methodology offers an efficient tool for handling the commercial traveler problem. Finally the optimal solution with in the kind of fuzzy numbers and justified its solution with in the nature of fuzzy membership functions.