By Andrzej Bielecki, Marzena Bielecka, Anna Chmielowiec (auth.), Leszek Rutkowski, Ryszard Tadeusiewicz, Lotfi A. Zadeh, Jacek M. Zurada (eds.)

This e-book constitutes the refereed complaints of the ninth overseas convention on man made Intelligence and smooth Computing, ICAISC 2008, held in Zakopane, Poland, in June 2008.

The 116 revised contributed papers provided have been conscientiously reviewed and chosen from 320 submissions. The papers are geared up in topical sections on neural networks and their functions, fuzzy structures and their functions, evolutionary algorithms and their purposes, category, rule discovery and clustering, photograph research, speech and robotics, bioinformatics and scientific functions, numerous difficulties of man-made intelligence, and agent systems.

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**Extra resources for Artificial Intelligence and Soft Computing – ICAISC 2008: 9th International Conference Zakopane, Poland, June 22-26, 2008 Proceedings**

**Example text**

W Hm 0 (m) g(m) (n) = 1 g1(m) (n) . . gH (n) m T , T = T (m) = 1 σ χ(m) 1 (n) . . σ χ1 (n) . (25) (m) From(3) it follows, that −1 ≤ σ χi (n) ≤ 1 so in consequence g(m) (n) H + 1. Hence the value of η (m) is bounded by following inequality: 0 < η (m) (n) < (24) 2 , Hm + 1 2 ≤ (26) which means that the greater number of neurons in hidden layer, the smaller permissible value of η (m) . In order to ﬁnd interval for η (m) , we have to evaluate (23) using (12) and (14). It is necessary to ﬁnd an upper bound of the recurrent (m) term Γh (n).

Condition 4a (the insertion of new neuron (n) between two neighbouring highactive neurons no. i and no. i+1): IF wini > β3 AND wini+1 > β3 THEN weight vector w (n) of new neuron (n) is calculated as follows: w (n) = w i +2w i+1 , where wini , wini+1 are as in Condition 1 and β3 is experimentally selected parameter (usually β3 is comparable to β1 that governs Condition 1). Conditions 4b (the replacement of high-active neuron no. i - accompanied by low-active neurons no. i−1 and no. i+1 - by two new neurons: (n) and (n+1)): IF wini > β3 AND wini−1 < β3 AND wini+1 < β3 THEN weight vectors w (n) and w (n+1) of new neurons (n) and (n+1) are calculated as follows: w (n) = w i−12+w i and w (n+1) = w i +2w i+1 (β3 - as in Condition 4a).

Further discussion will be also clear if we restrict to SISO systems (Lm = Sm = 1 for all m), see Fig. 3. All conclusions drawn in this paper can be strictly generalized to multivariate systems, but we want to keep complexity of notation on a reasonable level. As stated before, learning algorithm (6) ﬁnds suboptimal (from a point of view of performance index (5)) solution only when values of coeﬃcient η are selected properly at each time step n. Otherwise it diverges or oscillates ([8], [9], [10]).