Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
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Fuzzy set theory is investigated as a tool for the diagnostics of systems described by means of a fault tree. The objective is to diagnose component failures from the observation of fuzzy symptoms using the information contained in a fault tree. A two-step procedure is used to solve the problem. In this first step, causal reasoning is used to diagnose failure modes, consisting of minimal cut-sets of basic events, from the observation of triggered gates treated as symptoms. In the second step, the authors identify the particular components which have failed based on the diagnosed failure modes. To perform this second step, the solution of a fuzzy relational equation a= V-product (S/sup T/ alpha x) connecting failure mode a to basic events x is derived. With this method, the diagnostics equations can be symmetrically generated and solved in terms of the tree's basic events. The systematic nature with which a diagnosis can be generated from a fault tree lends this method to potential application of object-based programming techniques.