On Generalized Fuzzy Entropy and Fuzzy Divergence Measure with Applications

Entropy in a fuzzy set measures the amount of ambiguity/imprecision presented in the fuzzy set. In this article, the authors introduce a generalized fuzzy entropy measure and demonstrate its effectiveness in Multiple Attribute Decision Making (MADM) and superiority from the point of view of structured linguistic variables. This article also introduces a generalized fuzzy directed divergence and investigates its properties. Further, this article demonstrates the effectiveness of the proposed generalized directed divergence in pattern recognition.

Parametric R-norm directed-divergence convex function

In this paper, we define parametric [Formula: see text]-norm directed-divergence convex function and discuss their special cases and prove some properties similar to Kullback–Leibler information measure. From [Formula: see text]-norm divergence measure new information measures have also been derived and their relations with different measures of entropy have been obtained and give its application in industrial engineering.