Fuzzy universal generating functions for multi-state system reliability assessment

The paper considers a multi-state system (MSS) where performance rates or/and corresponding state probabilities are presented as fuzzy values. In many real world MSSs it is difficult to estimate precise values of performance rates and their probabilities because of two main reasons. The first reason is inaccuracy and insufficiency of data. The second one is based on the fact that MSSs are often used as the approximation for continuous-state systems in order to simplify computational burden. To overcome these deficiencies, performance rates (levels) or/and corresponding probabilities are considered as fuzzy values in this paper. The fuzzy universal generating function (FUGF) is developed to extend the universal generating function with crisp sets. The composition operators are extended for FUGFs and introduced in more general forms. Based on this a special technique for reliability assessment of such MSSs is developed. Illustrative examples are presented to demonstrate the technique.