Fuzzy Neurons Fuzzy model of artificial neuron can be constructed by using fuzzy operations at single neuron level y=g(w.x) 2 % Xn X (X1,X2…Xn) W= (W1,W2,…Wn)
Fuzzy Neurons ◼ Fuzzy model of artificial neuron can be constructed by using fuzzy operations at single neuron level x = (x1,x2,… xn) w = (w1,w2,… wn) y= g(w.x)
Fuzzy Neurons X y=g(w.x) y g(A(W,x)) Instead of weighted sum of inputs,more general aggregation function is used Fuzzy union,fuzzy intersection and,more generally. s-norms and t-norms can be used as an aggregation function for the weighted input to an artificial neuron
Fuzzy Neurons y = g(w.x) y = g(A(w,x)) ◼ Instead of weighted sum of inputs, more general aggregation function is used ◼ Fuzzy union, fuzzy intersection and, more generally, s-norms and t-norms can be used as an aggregation function for the weighted input to an artificial neuron
OR Fuzzy Neuron X AND W. X2AND W2 0R:[0,1]x[0,1]n->[0,1] OR y X AND Wn y=OR(X1 AND W1,X2 AND W2 ..Xn AND Wn) Transfer function g is linear If wk=0 then wk AND Xk-0 while if wk=1 then wk AND Xk=Xk independent of xk
OR Fuzzy Neuron ◼ Transfer function g is linear ◼ If wk=0 then wk AND xk=0 while if wk=1 then wk AND xk= xk independent of xk y=OR(x1 AND w1 , x2 AND w2 … xn AND wn) OR:[0,1]x[0,1]n->[0,1]