Fuzzy rule-based reliability analysis using NSGA-II

Abstract

Practically, reliability-based system designs are modeled in various kinds of uncertainty such as expert’s information character, qualitative statements, vagueness, etc. Fuzzy set theory is suitable for tackling such types of uncertainty effectively. In most of the practical situations, where reliability enhancement is an essential requirement, decision-making is a complicated task due to the presence of several mutually conflicting objectives such as system’s cost, weight, and volume. To solve such problems, multi-objective evolutionary algorithms (MOEAs) are efficient techniques for finding multiple Pareto-optimal solutions in a single simulation run. This paper applies an elitist MOEA, namely, NSGA-II to fuzzy multi-objective reliability optimization problem consisting of conflicting objectives such as system reliability and its cost. Linguistic hedges (or modifiers) are used to modify the Pareto-optimal solution set obtained by NSGA-II in terms of the membership grades of the objective values. The max–min composition of the membership grades gives the maximum satisfaction level to each possible combination of the linguistic hedges. After that, fuzzy rule-based system (FRBS) is proposed for evaluating the system efficiency to each case which is used in the decision-making of reliability. A numerical example is given to illustrate the method. Finally, the proposed approach is comparatively studied with the existing approach.