Abstract: Distance measure is a basic and crucial notion of set theory. Since the intuitionistic fuzzy sets (IFSs) were put forward, distance between IFSs has been widely concerned by some researchers and many types of measures have been proposed. Most of them have counter-intuitive cases and ignore the characteristics of three parameter properties of IFSs. The concept of fuzzy distance was introduced, which embodied the characteristics of classical distance and highlights the characteristics of hesitance index simultaneously. A new fuzzy distance measure was proposed, and the corresponding proof was included. An artificial benchmark test set of distance measure was constructed based on single-element IFSs, which was applied to compare the proposed distance measure with the widely used distance measures. Results show that the proposed distance does not provide any counter-intuitive cases and the waver that brought from hesitancy degree can be well reflected.

Key words: fuzzy distance, Intuitionistic fuzzy sets, Distance, Pattern recognition