Orthogonal Fuzzy Rule-Based Systems: Selection of Optimum Rules

In this paper, the concept of orthogonal fuzzy rule-based systems is introduced. Orthogonal rules are an extension to the definition of orthogonal vectors when the vectors are vectors of membership functions in the antecedent part of rules. The number and combination of rules in a fuzzy rule-based system will be optimised by applying orthogonal rules. The number of rules, and subsequently the complexity of the fuzzy rule-based systems, are directly associated with the number of input variables and distinguishable membership functions for each individual input variable. A subset of rules can be used if it is known which subset provides closer behaviour to the case when all rules are used. Orthogonal fuzzy rule-based systems are proposed as a judgment as to whether the optimal rules are selected. The application of orthogonal fuzzy rules becomes essential when fuzzy rule-based systems containing many inputs are used. An illustrative example is presented to create a model for the solder paste printing stage of surface mount tech-nology.