Probabilistic Entropy Measure Derived by using Quadratic Polynomials and their properties

Abstract

First, C. E. Shannon introduced Shannon's entropy, an entropy measure in communication theory. This
measure is logarithmic in nature. In order to quantify information uncertainty, various academics developed new
logarithmic and exponential entropy metrics after Shannon. In this study, a novel probabilistic entropy measure that
efficiently measures complexity and uncertainty in complex systems is proposed using the quadratic equation. These
novel probabilistic entropy Metrics have a big impact on how we understand complicated systems and how we make
decisions in many fields. Several established entropy axioms have been used to verify the validity of the new
probabilistic entropy measure. The findings show that quadratic entropy metrics perform better than current ones in
capturing minute variations in system uncertainty and behavior. In this paper, we discuss some properties of this
measure.