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Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

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in a set need not be always binary but may assume any value between zero <strong>and</strong><br />

one. In fuzzy logic Max, Min, composition, t- norm, s- norm, <strong>and</strong> other<br />

operators are used along with fuzzy sets to h<strong>and</strong>le real world reasoning<br />

problems. Fuzzy logic has been successfully used for modeling artificial neural<br />

nets, [19] where the input <strong>and</strong> output parameters of the neural net are the<br />

membership distributions.<br />

Among the classical fuzzy neural nets, the OR-AND neuron model of<br />

Pedrycz [19] needs special mention. In an OR-AND neuron, we have two OR<br />

nodes <strong>and</strong> one AND node [vide fig. 14.13].<br />

Here, Z1 = ∧ ( Wij ∨ xj)<br />

1 ≤ j≤ n<br />

Z2 = ∨ ( Vij ∧ xj)<br />

1 ≤ j≤ n<br />

<strong>and</strong> y= (S11 ∧ Z1 ) ∨ (S12 ∧ Z2 )<br />

where 'Λ' <strong>and</strong> 'V' denote fuzzy 't' <strong>and</strong> 's' norm operators. The above two<br />

operations are executed by using expressions (14.12) <strong>and</strong> (14.13).<br />

x1 Λ x2 = x1.x2 (14.12)<br />

x1 V x2 = (x1+x2−−−− x1.x2) (14.13)<br />

where '.' <strong>and</strong> '+' are typical algebraic multiplication <strong>and</strong> summation operations.<br />

Pedrycz devised a new algorithm for training an AND-OR neuron, when<br />

input membership distributions xi for i =1 to n <strong>and</strong> target scalar y are given.<br />

The training algorithm attempts to adjust the weights, wi j, so that a pre-defined<br />

performance index, is optimized.<br />

Pedrycz also designed a pseudo-median filter for using AND-OR<br />

neurons, which has many applications in median filtering under image<br />

processing. The typical organization of a pseudo-median filter for five delta<br />

points is given in fig.14.14.

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