Artificial Intelligence: Summary and Hybrid Schemes - Digital Signal Processing in Power System Protection and Control - page 308

• Fuzzy AND neuron

y ¼ AND ð p 1 ; ... ; p n Þ¼ T ð p 1 ; ... ; p n Þ¼ TS ð w 1 ; x 1 Þ ; ... ; S ð w n ; x n Þ ð Þ ð 15 : 2 Þ

with T = min, S = max (min-max composition):

y ¼ min w 1 _ x 1 ; ... ; w n _ x n ð Þ ð 15 : 3 Þ

• Fuzzy OR neuron

y ¼ OR ð p 1 ; ... ; p n Þ¼ S ð p 1 ; ... ; p n Þ¼ ST ð w 1 ; x 1 Þ ; ... ; T ð w n ; x n Þ ð Þ ð 15 : 4 Þ

with T = min, S = max (max-min composition)

y ¼ max w 1 ^ x 1 ; ... ; w n ^ x n ð Þ ð 15 : 5 Þ

• implication-OR fuzzy neuron

y ¼ SI ð w 1 ; x 1 Þ ; ... ; I ð w n ; x n Þ ð Þ ð 15 : 6 Þ

• Kwan and Cai's max fuzzy neuron

e ¼ u max w 1 x 1 ; ... ; w n x n ð ð Þ H Þ ð 15 : 7a Þ

y ¼ l ð e Þ ð 15 : 7b Þ

• Kwan and Cai's min fuzzy neuron

e ¼ u min w 1 x 1 ; ... ; w n x n ð ð Þ H Þ ð 15 : 8a Þ

y ¼ l ð e Þ ð 15 : 8b Þ

With last two neurons fuzzification is obtained with introduction of the fuzzy
membership function l.

15.2.2 Cooperative Hybrid Schemes

In the case of cooperative hybrid systems, any of the AI technique employed is
assigned to work independently from the others. Their inputs/outputs can be
exchanged, which usually results in cascaded connections of sub-schemes, rarely
some other connection versions can be met. The AI techniques applied cooperate,
but do not permeate each other.
The most popular for applications in protection and control are the schemes
employing neural networks and /fuzzy-logic set theory. Numerous examples can