New Ranking Approach of Intuitionistic Fuzzy Sets and its Application in Cognitive Transportation Problem

Abstract

In real-life problems, we frequently face uncertain situations because of human cognitive behaviour. Researchers have suggested meticulous mathematical notions to tackle such situations since its initiation. An intuitionistic fuzzy set is one of the effective extensions of a fuzzy set. Intuitionistic fuzzy sets have been applied in various real-life cognitive decision-making problems, for instance, engineering, medicine, pattern recognition, transportation, criminal investigation, etc. Numerous research works can be found in the literature, and most had several restrictions or were performed as unfit for providing human satisfaction outcomes. This work proposes a way to rank intuitionistic fuzzy sets using membership and non-membership functions. We discuss the benefits and provide examples to illustrate the approach. Then, we use our proposed ranking approach to deal with cognitive transportation problems, as it is well known that the core objective of transportation problems is to find optimal solutions. The literature contains various research studies on intuitionistic fuzzy problems with transportation. However, most of them have drawbacks.. Some methods are impractical, and others can't meet supply and demand limitations.. As a result, a method has been developed to lessen restrictions on solving methods of the intuitionistic fuzzy transportation problem. Although, some existing transportation problems are depicted in this work for a comparative study to elaborate on the significance of the present work. Our work deals with solving transportation problems in different uncertain situations using intuitionistic fuzzy environments like normal mixed type triangular, fully triangular and generalized trapezoidal intuitionistic fuzzy.. At the end of the study, hesitancy, cost effectiveness, statistical significant, sensitivity, result analysis, computational complexity and advantages are discussed to establish the effectiveness of the proposed work.