Overview of Diverse Entropy Measures

Author(s)	Anuradha Swarnkar, Dr. Rohit Verma
Country	India
Abstract	Entropy arises in many contexts as a quantifier of discrete properties, motivating families of entropy measures tailored to specific distributions. In this work, we develop measures based on the Rayleigh and truncated Rayleigh laws and, in parallel, derive Shannon-type entropies under an exponential-power generalization of the normal (Gaussian) distribution. We also introduce a new generalized entropy measure and summarize its key mathematical properties. Additionally, we present a generalized hyperbolic form of probabilistic entropy that exhibits strong additive behavior and rapid adaptability across modeling scenarios. Extending into fuzzy information frameworks, the paper connects these ideas to non-classical (non-Boolean) data theories and discusses a generalized Fisher-type information/entropy measure. Finally, we define two entropy formulations for complex fuzzy sets, Type-A, which depends solely on membership amplitude, and Type-B, which incorporates both amplitude and phase, and assess their rotational invariance, clarifying when these measures remain unchanged under phase rotations.
Published In	Volume 7, Issue 5, September-October 2025
Published On	2025-10-31
DOI	https://doi.org/10.36948/ijfmr.2025.v07i05.59455

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