Uncertainty and fuzziness are involved in most of the real world problems. In present communication we have studied various advancements in fuzzy information theory and proposed a new measure of divergence between two fuzzy sets. Further, a measure of fuzzy directed divergence was developed based on the proposed divergence measure. Some properties of this fuzzy directed divergence measure were ...

In arbitrage-free but incomplete markets, the equivalent martingale measure Q for pricing traded assets is not uniquely determined. A possible approach when it comes to choosing a particular pricing measure is to consider the one that is ‘closest’to the physical probability measure P, where closeness is measured in terms of relative entropy. In this paper, we determine the minimal entropy marti...

The present paper introduces a parametric generalized exponential measure of fuzzy divergence of order α with the proof of its validity. A particular case of proposed fuzzy divergence measure is studied. Some properties of the new divergence measure between different fuzzy sets are proved. We establish a relation between exponential fuzzy entropy of order α and our fuzzy divergence measure. Fur...

We analyze a class of L∞ vector fields, called divergence-measure fields. We establish the Gauss-Green formula, the normal traces over subsets of Lipschitz boundaries, and the product rule for this class of L∞ fields. Then we apply this theory to analyze L∞ entropy solutions of initial-boundary-value problems for hyperbolic conservation laws and to study the ways in which the solutions assume t...

We have considered one parametric generalization of the nonsymmetric relative J-divergence measure. The generalized measure is shown belonging to the Csiszár’s f-divergence class. Further, we have derived bounds for the generalized measure in terms of well known divergence measures.