Distances

Abstract

In many theoretical and practical issues we face the following problem. Having two sets in the same universe, we want to calculate a difference between them exemplified by a distance. In this Chapter we consider distances between the intuitionistic fuzzy sets in two ways: while using the two term intuitionistic fuzzy set representation (membership values and non-membership values only are taken into account), and the three term intuitionistic fuzzy set representation (membership values, non-membership values, and hesitation margins are taken into account). We discuss norms and metrics for both types of representations. Both types are correct from the mathematical point of view but, in the practical perspective, the three term approach seems to be more justified. We discuss the problem in detail, considering its analytical, and geometrical aspects. We also show some problems with the Hausdorff distance, while the Hamming metric is applied when using the two term intuitionistic fuzzy set representation. We also show that the method of calculating the Hausdorff distances, which is correct for the interval-valued fuzzy sets, does not work for the intuitionistic fuzzy sets. Finally, we show the usefulness of the three term distances in a measure for ranking the intuitionistic fuzzy alternatives.