By Didier Dubois, Henri Prade (auth.), Prof. Dr. Bernd Reusch, Dr. Karl-Heinz Temme (eds.)
Computational Intelligence with its roots in Fuzzy good judgment, Neural Networks and Evolutionary Algorithms has turn into an incredible learn and alertness box in computing device technology within the final decade. Methodologies from those parts and combos of them permit clients from engineering, company, drugs and lots of extra branches to trap and strategy imprecise, incomplete, doubtful and vague information and data. Many algorithms and instruments were constructed to resolve difficulties within the nation-states of low and high point regulate, details processing, diagnostics, selection help, category, optimisation and plenty of extra. This e-book attempts to teach the influence and suggestions among idea and purposes of Computational Intelligence, highlighted on chosen examples.
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Additional info for Computational Intelligence in Theory and Practice
D. Butnariu and E. P. Klement. Triangular Norm-Based Measures and Games with Fuzzy Coalitions. Kluwer, Dordrecht, 1993 7. H. Clifford. Naturally totally ordered commutative semigroups. Amer. J. , 76:631-646,1954. 8. C. Climescu. Sur 1'equation fonctionelle de 1'associativite. Bull. l:I-16. 1946. 9. J. Dombi. A general class of fuzzy operators, De Morgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets and Systems. 1982. 10. D. Dubois. Triangular norms for fuzzy sets.
Proposition 5. 3. (i) Let T be t-norm. Then T[OPI = T for any increasing bijection cp if and only if T is either TM or Tw. (ii) Tp = (Tp) [opl jf and only if
0. (iii) T L = (TU [opl if and only if cp(x) = x. The isomorphism cp preserve the properties of given T. So, e. , if T is i) continuous, ii) non-continuous, iii) strict, iv) non-strict, v) nilpotent, vi) nonnilpotent, vii) Archimedean, viii) non-Archimedean, ix) without zero-divizors, x) with zero-divizors, all of these properties are fulfilled also by T [opl whenever cp is an isomorphism.
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