A Basic Approach to Reduce the Complexity of a Self-generated Fuzzy Rule-Table for Function Approximation by Use of Symbolic Regression in 1D and 2D Cases
There are many papers in the literature that deal with the problem of the design of a fuzzy system from a set of given training examples. Those who get the best approximation accuracy are based on TSK fuzzy rules, which have the problem of not being as interpretable as Mamdany-type Fuzzy Systems. A question now is posed: How can the interpretability of the generated fuzzy rule-table base be increased? A possible response is to try to reduce the rule-base size by generalizing fuzzy-rules consequents which are symbolic functions instead of fixed scalar values or polynomials, and apply symbolic regressions technics in fuzzy system generation. A first approximation to this idea is presented in this paper for 1-D and 2D functions.
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