A Novel Ranking Approach to Rank Interval-Valued Trapezoidal Intuitionistic Fuzzy Sets by Using the Concept of Centroids

An Interval-valued trapezoidal intuitionistic fuzzy set (IVTrIFS) is a powerful tool for modelling uncertainty. The ranking of IVTrIFSs plays a vital role in fuzzy set theory to compare and analyze the given information. An IVTrIFS is a special type of Intuitionistic Fuzzy Set (IFS) and interval-valued intuitionistic fuzzy set (IVIFS) with a consecutive domain of real numbers. In this paper, we analyzed many ranking methods based on various Fuzzy logic techniques and proposed a new ranking method from geometric point of view, the expectation and expectant score function of an IVTrIFS from the concept of centroids of the membership function, non-membership function, and hesitancy function. The comparative results show that the proposed method is innate and effective, very useful to the applications of computational Intelligence, decision-making, predictive system analysis, and performance analysis.