Strict intuitionistic fuzzy distance/similarity measures based onJensen-Shannon divergence

Abstract Being a pair of dual concepts, the normalized distance and similarity measures are important tools fordecision-making and pattern recognition under an intuitionistic fuzzy set framework. A good normalizeddistance measure should ensure that its dual similarity measure satisfies the axiomatic definition in orderto be more effective for problems. In this paper, we first construct some counterexamples to illustrate thattwo existing measures do not meet the axiomatic definition of intuitionistic fuzzy similarity measures.We then show that (1) these two measures cannot effectively distinguish some intuitionistic fuzzy values(IFVs), which can be directly judged by our intuition; (2) except for the endpoints, there exist infinitelymany pairs of IFVs, where the maximum distance 1 can be achieved under these two distances, leading tocounter-intuitive results. To overcome these drawbacks, we introduce the concept of strict intuitionisticfuzzy distance measure (SIFDisM) and strict intuitionistic fuzzy similarity measure (SIFSimM), andpropose an improved intuitionistic fuzzy distance measure based on Jensen-Shannon divergence. Weprove that (1) it is a SIFDisM; (2) its dual similarity measure is a SIFSimM; (3) its induced entropyis an intuitionistic fuzzy entropy. Comparative analysis and numerical examples demonstrate that ourproposed distance measure is completely superior to the existing ones.