A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis

Abstract

The intuitionistic fuzzy set, as a generation of fuzzy set, can express and process uncertainty much better. Distance measures between intuitionistic fuzzy sets are used to indicate the difference degree between the information carried by intuitionistic fuzzy sets. Although some distance measures have been proposed in previous studies, they can not satisfy the axioms of distance measure, or exist counter-intuitive cases. In this paper, we give a new distance measure between intuitionistic fuzzy sets, which is based on a matrix norm and a strictly increasing (or decreasing) binary function. The new distance measure not only satisfies the axiomatic definition of distance measure, but also overcomes the counter-intuitive cases. It is proved that the new distance measure is reasonable by numerical examples. Moreover, we give the algorithms for pattern recognition and use it to solve medical diagnosis problems.

Keywords: Distance measures; Intuitionistic fuzzy sets; Pattern classification.