An efficient computational approach for solving type-2 intuitionistic fuzzy numbers based Transportation Problems

Abstract

This paper is concerned with the solution procedure of a Transportation Problem in which costs are tri- angular intuitionistic fuzzy numbers (TIFN) and availabilities and demands are taken as exact numerical values. According to the existing solution approach, TIFN are first ordered by using an accuracy function defined on score functions for membership and non-membership functions of TIFN. Then this order- ing is used to develop methods for finding an initial basic feasible solution and the optimal solution of intuitionistic fuzzy Transportation Problems in terms of triangular intuitionistic fuzzy numbers. This so- lution approach, in spite of its merits, requires a lot of fuzzy arithmetic operations, such as additions and subtractions of TIFN, as well as a lot of comparisons on TIFN. In this paper an efficient computational solution approach is proposed for solving intuitionistic fuzzy Transportation Problems based on classical transportation algorithms to overcome the shortcomings of the aforementioned solution approach. In the approach here presented, the comparison of triangular intuitionistic fuzzy costs is done once and all arith- metic operations are done on real numbers. Finally, for the sake of illustration, two intuitionistic fuzzy Transportation Problems are solved herein to demonstrate the usages and advantages of the proposed solution approach.