Application of Extended Fuzzy Programming Technique to a real life Transportation Problem in Neutrosophic environment

Abstract

Here This paper focuses on solving the transportation problems with neutrosophic data for the first time. The indeterminacy factor has been considered in Transportation Problems (TP). The two methods of linear programming – Fuzzy Linear Programming (FLP) and Crisp Linear Programming (CLP) are discussed with reference to neutrosophic transportation problems. The first method uses the membership, non-membership and indeterminacy degrees separately to find the crisp solution using the Fuzzy Programming Technique and then the optimal solution is calculated in terms of neutrosophic data with the help of defined cost membership functions. The satisfaction degree is then calculated to check the better solution. The second method directly solves the TP to find a crisp solution considering a single objective function. The cost objective function is taken as neutrosophic data and the methods have been used as such for the first time. Both the methods have been illustrated with the help of a numerical example and these are then applied to solve a real-life multi-objective and multi-index transportation problem. Finally, the results are compared.