Fuzzy Control Architectures

In this article we analyze the process of executing the knowledge base KB of a fuzzy control system following the “Sup-*” compositional rule of inference [Zadeh LA 1973: “Outline of a new approach to the analysis of complex systems and decision processes.” IEEE Trans. Syst. Man Cybern. 31: 28--44]. From the expressions obtained, two different methodologies are derived: rule by rule and global implication matrices. Two systolic architectures following these methodologies are proposed using a partitioning and projection technique. Both architectures permit executing any KB independently from the size parameters that characterize it, such as number of rules, number of antecedents and consequents, and discretization degree of the universes of discourse. The solutions also present great flexibility with respect to the operators implementing the inference process implication and conjunction functions and “*” t-norm. The selection of one of these solutions is conditioned by the particular features of the system to be controlled: the relationship between the parameters that characterize the KB and the most adequate reasoning mechanism to carry out the control process. The need to achieve a compromise between operational speed, flexibility of the reasoning mechanism, and complexity of the KB will determine the selection of one solution or the other for each specific case.

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