A study of defuzzification with experts' knowledge for deteriorating repairable systems

Abstract

This paper presents ideas on the applications of fuzzy concepts to decision making for deteriorating repairable systems. A non-homogeneous Poisson process (NHPP) with a power-law intensity function is used in this study. In general, classical Bayesian decision methods presume that future states of nature can be characterized as probability events. However, we do not know what the future will entail probabilistically, so we devise a method to consider experts' opinions, which are usually the absence of sharply defined criteria, and to develop a fuzzy Bayesian decision process for dealing with such situations. Two cases of the discrimination problem with deteriorating repairable systems are studied: (1) fuzzy states and exact information and (2) fuzzy states and fuzzy information. The fuzzy decomposition and arithmetic derivation of the experts' opinion are presented to facilitate the development of the Bayesian decision process for deteriorating repairable systems.