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By Japan) International Conference on Soft Computing 1998 (Iizuka-Shi

Delicate computing (SC) comprises numerous computing paradigms, together with neural networks, fuzzy set concept, approximate reasoning, and derivative-free optimization equipment corresponding to genetic algorithms. the mixing of these constituent methodologies kinds the middle of SC. furthermore, the synergy permits SC to include human wisdom successfully, care for imprecision and uncertainty, and discover ways to adapt to unknown or altering environments for larger functionality. including different smooth applied sciences, SC and its functions exert unparalleled impact on clever platforms that mimic human intelligence in considering, studying, reasoning, and lots of different elements. wisdom engineering (KE), which offers with wisdom acquisition, illustration, validation, inferencing, clarification and upkeep, has made major growth lately, as a result of the indefatigable efforts of researchers. absolutely, the recent subject matters of information mining and knowledge/data discovery have injected new existence into the classical AI international. This booklet tells readers how KE has been motivated and prolonged via SC and the way SC may be precious in pushing the frontier of KE additional. it truly is meant for researchers and graduate scholars to exploit as a reference within the examine of information engineering and clever structures. The reader is predicted to have a easy wisdom of fuzzy common sense, neural networks, genetic algorithms and knowledge-based platforms.

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Extra resources for A New Paradigm of Knowledge Engineering by Soft Computing (Fuzzy Logic Systems Institute (Flsi) Soft Computing Series, Volume 5)

Example text

Associate linguistic labels to the resulting membership functions. With the partition of the output universe, fuzzify the values of the singletons. Observe that each singleton will have a membership degree in at least one set and in as much as two. Relate the fuzzified values with the corresponding rule. It means that each rule will have one consequence or two weighted consequences were the weights are the non zero membership values of the fuzzified singleton. This conversion of the singleton consequences into weighted triangular consequences gives linguistic meaning to the consequences.

The system then can be represented as the weighted sum of the consequences: f(uk) =^2wf(uk)yt (17) tof(Ufc) = (18) where L i=i expressing wf as the strength of the rule I when the input is u*. Taking all the values the problem can be seen as: 1 y\ -1 2 w, 2/2 N L WX N WL J < " 2/i ei 2/2 &2 . VL . + (19) . ew . w The aim here is to reduce as much as possible the norm of the vector E. Using the quadratic norm: mm||E|| 2 = m i n | | y - W 0 | | 2 (20) Linguistic Integrity: A Framework for Fuzzy Modeling .

3 *,JV^ " * (10) *=i, (6) Construct the triangular membership functions with overlap of | as: nKx3) = max 0,min m:»+i '»-i m^ l i-i m^ (11) m:« + i , where: i = 1 , . . i (12) - • (13) l c+i TUr (7) Apply PuZion algorithm to reduce the number of membership functions. The FuZion algorithm guarantees a reduction of the membership functions till they fulfill the requirements of "distinguishability" and "justifiable number of elements". ) to the resulting membership functions. (9) Construct the rule base with all possible antecedents (all possible permutations).

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