Analysis of distance measures in intuitionistic fuzzy set theory: A line integral perspective

Abstract

The distance between the intuitionistic fuzzy sets (IFSs) is a notable and has been widely used information measure to enhance decision-making performance. However, different numerical results are derived when using different distance measures. Therefore, it is worthwhile to explore in depth how to select an appropriate formula for distance computation. This paper uses the line integral to define the distance between IFSs. The presented study divided into three folds. First, the existing distances between IFSs are examined, and their flaws are listed. Second, the distances between IFSs are redefined based on the analysis of the geometric importance of the line integral. More importantly, some existing distances happen to be special cases of the distance we define. Finally, we introduce the accuracy function into the defined distance for evaluating the accuracy of distance by applying the physical meaning of line integral. In other words, the distance accuracy is emphasized as a crucial standard by which to assess the effectiveness of distances between IFSs. To demonstrate the stated measures, some numerical examples are provided to show the superiority of our approach.