Diagnosis based on multivariable fuzzy relations
Abstract
This paper deals with restoration of the causes (diagnoses) through the observed effects (symptoms) on the basis of multivariable fuzzy relations and the extended compositional rule of inference. The design of a diagnostic fuzzy system consists of solving fuzzy relational equations together with tuning of fuzzy relations on the basis of information from experts and experiments. We propose a method for solving fuzzy relational equations with the extended max-min composition. We also prove the properties of the solution set for such systems. The problem of finding the solution set is formulated in the form of the optimization problem, which is solved using genetic algorithms and neural networks. The essence of tuning consists of the selection such membership functions for fuzzy causes and effects, and also fuzzy relations, which minimize the difference between model and experimental results of a diagnosis. The proposed approach is illustrated by the computer experiment and the example of a technical diagnosis.References
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