The Fusion of Discrete Z-Numbers With Application for Fault Diagnosis

A Z-number, which is a generalization of probability and fuzzy numbers, is a novel model to represent uncertainty in the real world. This article aims to develop discrete Z-numbers in both theory and application with the methodology of information fusion. First, a method for the fusion of discrete Z-numbers is proposed, in which the following problems are solved: 1) the extension principle and linear smoothing operator are used to obtain reasonable possibility distributions and 2) an optimization model based on the maximum entropy is constructed to obtain the most likely underlying probability. Thus, the relationship between the two components of Z-numbers is considered in our method. Second, the fusion of Z-numbers is applied to data-driven fault diagnosis, with which we show the potential of Z-numbers in real data in addition to linguistic information. The effectiveness of the proposed method is illustrated by the numerical experiments, where the two components of Z-numbers are generated according to their interpretations.