A New Type-2 Intuitionistic Exponential Triangular Fuzzy Number and Its Ranking Method with Centroid Concept and Euclidean Distance

This paper introduces a new type-2 intuitionistic exponential triangular fuzzy number. Basic generalized exponential triangular intuitionistic fuzzy numbers are formulated by (α, β)-cuts. Some of properties and theorems of this type of fuzzy number with graphical representations have been studied and some examples are given to show the effectiveness of the proposed method. Also, the ranking function of the generalized exponential triangular intuitionistic fuzzy number is computed. This ranking method is based on the centroid concept and Euclidean distance. Based on the ranking method, we develop an approach to solving an intuitionistic fuzzy assignment problem where cost is not deterministic numbers but imprecise ones. Then, we solve an intuitionistic fuzzy transportation problem where transportation cost, source, and demand were generalized type-2 intuitionistic fuzzy numbers by the ranking method for Euclidean distance. Intuitionistic fuzzy set theory has been used for analyzing the fuzzy system reliability. We have taken the intuitionistic fuzzy failure to start of an automobile as known basic fault events such as Ignition failure, Battery internal shortage, Spark plug failure and fuel pump failure using Type-2 Intuitionistic Exponential Triangular Fuzzy Number. Our computational procedure is very simple to implement for calculations in intuitionistic fuzzy failure. The major advantage of using Intuitionistic fuzzy sets over fuzzy sets is that intuitionistic fuzzy sets separate the positive and the negative evidence for the membership of an element in a set. Furthermore, the proposed technique can be suitably utilized to solve the start of an automobile problem, because the result of system failure in this method is significant. Finally, the proposed method has been compared with other existing method through numerical examples.