A new distance measure of interval-valued intuitionistic fuzzy sets and its application in decision making

Interval-valued intuitionistic fuzzy sets are widely used in multi-attribute decision-making problems to select the optimal alternative, but how to measure uncertainty is an open and significant problem. In this paper, a new distance measure of interval-valued intuitionistic fuzzy sets is proposed based on the distance of interval numbers. With the advantages of taking account of the whole number in the interval and having definite physical meaning, the proposed distance measure of interval-valued intuitionistic fuzzy sets shows superiority in measuring uncertainty and imprecision. In addition, the proposed distance measure is compared with some recent research works and classical distances through numerical examples. Graphs are drawn to visually display the variation characteristics and analyze the properties of the distance measures. The results prove that the proposed distance measure of interval-valued intuitionistic fuzzy sets outperforms other metrics in measuring uncertainty and avoiding counterintuitive cases. Some illustrative examples of multi-attribute decision making under real life are conducted, which demonstrates the strong discrimination capability and effectiveness of the proposed distance measure.