A New Method to Find the Balanced Solution to the Transportation Problem with Fuzzy Sets of Type-2 for Supply and Demand

Abstract

The Transportation Problem is a fundamental problem widely studied in the Operational Research domain. The main objective of this paper is to contribute to a deeper study of the topics of fuzzy transportation problems of linear programming when the supply and demand are represented as a fuzzy set of type-2. Here, we are using a newly proposed method to solve a transportation problem with fuzzy sets type-2 of supply and demand to find a balanced solution. The membership function of a fuzzy set of type-2, which is the set of its feasible solutions, is constructed. The properties of this set are investigated, and the problems of choosing balanced solutions are considered. The newly proposed method of the fuzzy transportation problem is discussed with the help of an illustrative numerical example.