An optimization of the fully fuzzy transportation problem with triangular type-2 fuzzy parameters using novel ranking technique

Abstract

This paper focuses on solving the fully fuzzy transportation problem in which the parameters are triangular Type-2 fuzzy numbers due to the instinctive of human imprecision. To deal with uncertainty more precisely, a triangular Type-1 fuzzy transportation problem is reformed as a transportation problem with triangular Type-2 fuzzy parameters in this paper. In order to compare triangular Type-2 fuzzy numbers, a new ranking(ordering) technique is proposed by extending the Yager’s function. However, two efficient algorithmic approaches namely, triangular Type-2 fuzzy zero suffix method (TT2FZSM) and triangular Type-2 fuzzy zero average method (TT2FZAM) are proposed to generate the initial transportation cost of the fully triangular Type-2 fuzzy transportation problem. Both TT2FZSM and TT2FZAM are converging towards an optimal solution. In addition to TT2FZSM and TT2FZAM, the modified distribution method is applied to ensure optimality. Subsequently, we carry out a comprehensive discussion of the obtained results to establish the validation of the proposed approach.