Average duo triangle ranking technique to solve fully and type-2 intuitionistic fuzzy transportation problem

Abstract

In solving fuzzy transportation problem, ranking of a fuzzy number is a challenging task. Various methods are available in literature to rank a fuzzy number. But, most of these are problem specific; this motivates researchers to develop a vigorous ranking approach. The key idea of this paper is to propose a new ranking technique based on average of duo-triangle to solve fully and type-2 intuitionistic fuzzy transportation problem. The weightage is given to the portions which have higher membership grades in set of belonging. Then average of two triangles covering the major area of membership is calculated to get the ranked value. Thus, the obtained classical transportation problem is solved using north-west corner rule as well as minimum demand supply method. Optimality is tested through modified distribution technique. The proposed method yields the result in crisp value which is easy to understand and well-organized. Numerical examples are given to demonstrate the presented algorithm. Comparative study with the other existing methods verifies the applicability of the proposed technique.