Entropy methods for definition of generalized characteristics of systems (Q1594347)

The authors proposed a new entropy for defining the generalized characteristics of systems. Let \(X = ( x_{ij}) (i=1,2, ..., n; j=1,2,..., m)\) be a matrix of system characteristics, and \(P = (p_1 , p_2 , ..., p_n)\) be a probability vector. The proposed entropy is of the form \(H(P) = P X X^{-T} P^T - m P P^T \), where \(X^{-T}\) denotes the transpose of the matrix composed of the reciprocals of the elements of \(X\). This proposed entropy generalizes the entropy \(H(P) = 1- \sum_{j=1}^m p_j^2\) and has many formal properties of the Shannon entropy.