Communications in Mathematics and Statistics ( IF 0.9 ) Pub Date : 2021-07-07 , DOI: 10.1007/s40304-020-00228-1 Ratika Kadian 1 , Satish Kumar 1
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).
中文翻译:
Jensen-Renyi's-Tsallis 模糊发散信息测度及其应用
在本文中,我们描述了与具有离散随机变量的两个分布相关的两个一般度量的总和。这些度量之一是对数的,而其他度量则包含变量的幂,称为 Renyi's-Tsallis 散度度量的联合表示。然后,我们提出了一种基于 Jensen-Renyi's-Tsallis 熵的散度测度,称为 Jensen-Renyi's-Tsallis 散度测度。它是 J-divergence 信息测度的推广。这种度量的一个无声特征是我们可以为每个概率分布分配相等的权重。这使得它对于决策问题的研究特别合理,其中权重可以是先验概率。此外,该想法已从概率泛化到模糊相似性/不相似性度量。除了验证所提出的措施外,还研究了它的一些关键特性。此外,建议措施的性能与一些现有措施形成对比。最后,在聚类分析、金融诊断和模式识别的背景下解决了一些说明性例子,证明了所提出的两个模糊集(FS)度量的实用性和充分性。