New Generalized ‘Useful’ Entropies using Weighted Quasi-Linear Mean for Efficient Networking

Entropies have significant importance in the field of information and communication theory. They have an essential role in measuring along with modeling the complexity and uncertainty of complex networks. The research paper aims at deriving new generalized ‘useful’ entropies using the concept of the quasi-linear mean. The derived generalized ‘useful’ entropies will prove to be effective for networks, where few links or edges have greater importance or utility than other links or nodes, thereby giving more weightage to them while analyzing the networks. Firstly, few entropies were analyzed using the concept of quasi-linearity. During analysis, the supra-extensive entropy was successfully ascertained as the quasi-linear mean of generalized information for the first time. To extend the idea of the quasi-linear mean for probability distributions with associated utilities, a new concept of weighted quasi-linear mean with utility has been conceptualized. The introduced concept is applied to derive a few existing as well as new generalized ‘useful’ entropies. The concept defined can be utilized to find the generalized ‘useful’ information measure corresponding to any generalized information measures that are the quasi-linear means of elementary or generalized information.