Jensen–Renyi’s–Tsallis Fuzzy Divergence Information Measure with its Applications

Abstract

In this paper, we have characterized the sum of two general measures associated with two distributions with discrete random variables. One of these measures is logarithmic, while others contains the power of variables, named as joint representation of Renyi’s–Tsallis divergence measure. Then, we propose a divergence measure based on Jensen–Renyi’s–Tsallis entropy which is known as a Jensen–Renyi’s–Tsallis divergence measure. It is a generalization of J-divergence information measure. One of the silent features of this measure is that we can allot the equal weight to each probability distribution. This makes it specifically reasonable for the study of decision problems, where the weights could be the prior probabilities. Further, the idea has been generalized from probabilistic to fuzzy similarity/dissimilarity measure. Besides the validation of the proposed measure, some of its key properties are also studied. Further, the performance of the proposed measure is contrasted with some existing measures. At last, some illustrative examples are solved in the context of clustering analysis, financial diagnosis and pattern recognition which demonstrate the practicality and adequacy of the proposed measure between two fuzzy sets (FSs).

Keywords

Fuzzy sets / Divergence measure / Similarity measure / Clustering analysis / Financial diagnosis