Knowledge-Based Design of ANNs

Abstract

Corollaries 3.1-3.10 in Chapter 3 provide a transformation between a FARB and an ANN. The ANN type (i.e., feedforward, first-order RNN, or second-order RNN), structure, and parameter values, are determined directly from the FARB structure and parameters. This suggests a novel scheme for knowledge-based design (KBD) of ANNs. Given the initial knowledge, determine the relevant inputs, denoted x₁,...,x _m , and the number of outputs. For each output, restate the initial knowledge in the form of an FRB relating some subset of the inputs {y₁, ..., y _k } ⊆ {x₁,...,x _m } to this output. In this FRB, each y _i must be characterized using two fuzzy terms. The Then-part of each rule must be decomposed as a sum a₀±a₁±...±a _k , where the signs are determined according to the If-part of the rule. More rules are added to the FRB, if necessary, until it contains 2 ^k fuzzy rules, expanding all the possible permutations of the input variables. The output of each added rule is again a linear sum of the a _i s with appropriate signs. MFs for each input variable are chosen such that (2.3) holds.