TY - CHAP
T1 - Knowledge-based design of ANNs
AU - Kolman, Eyal
AU - Margaliot, Michael
PY - 2009
Y1 - 2009
N2 - 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,...,xm] 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,...,yk} ⊆ {x1,..., xm} to this output. In this FRB, each yi must be characterized using two fuzzy terms. The Then-part of each rule must be decomposed as a sum ao ± a1 ±...± ak, 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 2k fuzzy rules, expanding all the possible permutations of the input variables. The output of each added rule is again a linear sum of the ai s with appropriate signs. MFs for each input variable are chosen such that (2.3) holds.
AB - 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,...,xm] 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,...,yk} ⊆ {x1,..., xm} to this output. In this FRB, each yi must be characterized using two fuzzy terms. The Then-part of each rule must be decomposed as a sum ao ± a1 ±...± ak, 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 2k fuzzy rules, expanding all the possible permutations of the input variables. The output of each added rule is again a linear sum of the ai s with appropriate signs. MFs for each input variable are chosen such that (2.3) holds.
UR - http://www.scopus.com/inward/record.url?scp=54849412567&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-88077-6_6
DO - 10.1007/978-3-540-88077-6_6
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AN - SCOPUS:54849412567
SN - 9783540880769
T3 - Studies in Fuzziness and Soft Computing
SP - 59
EP - 76
BT - Knowledge-Based Neurocomputing
A2 - Kolman, Eyal
A2 - Margaliot, Michael
PB - Springer Berlin Heidelberg
ER -