An Improved Similarity Measure for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application to Multi-Attribute Decision-Making Problem

In this article, a new similarity measure is discussed on interval-valued intuitionistic fuzzy values (IVIFVs). Here, the proposed similarity measure has been derived based on transformed intervals and its probability density functions, mean values, and standard deviations of IVIFVs. Based on the proposed similarity measure, several essential properties have been illustrated in this paper. Additionally, a new algorithm has been developed using the similarity measure of interval-valued intuitionistic fuzzy values (IVIFVs) to solve multi-attribute decision-making (MADM) problem. The proposed method is highly effective for solving various types of MADM problems. To demonstrate the effectiveness of the proposed similarity measure, a car selection problem has been considered, where the objective is to choose a suitable car for a decision maker from a set of alternatives evaluated under multiple criteria. In car selection, different features often involve conflicting criteria with imprecise data. Therefore, the proposed similarity measure of interval-valued intuitionistic fuzzy values assists in determining the best alternative among these conflicting criteria.