Intuitive distance for intuitionistic fuzzy sets with applications in pattern recognition

Distance is an important fundamental concept of the set theory. Since the intuitionistic fuzzy sets (IFSs) was put forward, distance between IFSs has been widely concerned by some researchers and many types of measures have been proposed. However, although intuitionistic fuzzy sets have the advantage of being able to consider waver (lack of knowledge), existing distance measures have not yet considered waver and most of them have counter-intuitive cases. To deal with this problem, this paper introduces the concept of intuitive distance for IFSs, which embodies the property requirements of classical distance measure and highlights the characteristics of intuitionistic fuzzy information. Then, a new intuitive distance measure for IFSs is proposed along with its proofs. After that, a comparative analysis between the intuitive distance measure and the existing distance measures is conducted based on an extended artificial benchmark test set, in which eleven pairs of single-element IFSs are used as an illustration of six typical counter-intuitive cases. Finally, the proposed distance measure is applied to deal with pattern recognition. Results show that the proposed distance does not provide any counter-intuitive cases and the waver that brought from hesitance index can be well reflected.