Some Results on Specificity of Possibility Distributions

Specificity of a possibility distribution is akin to the entropy of a probability distribution. It serves an essential purpose to zero in on the maximum probability observation. However, when we discuss the existing definition of possibility distribution, it lacks applicability in real-world problems; hence, specificity also becomes an underrated measure for gauging the degree of uncertainty in a possibility distribution. In this paper, we present new findings on the specificity of a possibility distribution, resulting from our research on data-based semantic information analysis in hybrid human-machine systems. In this research, we propose a new frequency-based possibility and probability measure and formalise a new method for fitting restrictions on data or information available in the system. We will demonstrate that the proposed formula is superior to existing specificity measures and discuss various applications of specificity measures in solving problems related to hybrid systems. We shall summarise this paper by providing a real-world application of the proposed measure.