In this paper, an attempt is made to prove that some similarity based
fuzzy systems can be found to behave as function approximators. A typical
similarity based fuzzy system is proposed and its behaviour is shown to have
the said property. It elucidates the connection between similarity relation and
similarity measure of fuzzy sets to fuzzy inference methodology. The concept of
similarity relation is used in fuzzification of crisp input values. Similarity
index is used in measuring approximate equality of fuzzy sets over a given
universe of discourse of a linguistic variable. The similarity between the
observation(s) and the antecedent of a rule is used in selecting rule(s) for
possible firing and also in modifying the relation between the antecedent and consequent
of the rule based on the specific observation. Inference is drawn through the
usual composition and subsequently by projecting the modified fuzzy restriction
acting on the variables of interest on the universe of the linguistic variable
in the consequent of the rule. A specificity based defuzzification scheme is
proposed for multiple-rule firing. It has been proved systematically that such
a similarity based fuzzy system can uniformly approximate continuous functions
to any desired degree of accuracy on a closed and bounded interval. Simulation
results are presented for the well-known dc-motor problem. A comparative study
is made to establish the validity and efficiency of the proposed similarity
based fuzzy system.
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