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A Fuzzy Measure Approach to Systems Reliability Modeling

Our objective here is to study the role that fuzzy measures can play in systems reliability modeling. We first introduce some basic ideas from fuzzy measure theory and then introduce some specialized ideas about fuzzy measures, cardinality index, and attitudinal character, which will later be useful in comparing systems reliability. Basic ideas of reliability modeling and the role of the system structure function are discussed. The system's signatures associated with a structure function are introduced and we show their relationship to expected time to system failure. We show how we can model a systems structure function using a fuzzy measure's. A description of the role of a measures cardinality index and attitudinal character in providing tools for comparing systems reliability is provided. We describe how to obtain a structure model of a complex system using aggregation operators and the measure representation of individual components.