By Derong Liu, Fei-Yue Wang

Computational Intelligence (CI) is a lately rising quarter in basic and utilized examine, exploiting a couple of complex info processing applied sciences that commonly embrace neural networks, fuzzy common sense and evolutionary computation. With an important obstacle to exploiting the tolerance for imperfection, uncertainty, and partial fact to accomplish tractability, robustness and occasional answer expense, it turns into obvious that composing equipment of CI might be operating at the same time instead of individually. it really is this conviction that examine at the synergism of CI paradigms has skilled major development within the final decade with a few parts nearing adulthood whereas many others final unresolved. This e-book systematically summarizes the newest findings and sheds gentle at the respective fields that may result in destiny breakthroughs.

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Pedrycz, Granular Computing: An Introduction, Dordrecht: Kluwer Academic Publishers, 2002. 20 W. Pedrycz [2] Z. Bubnicki, "Uncertain variables and their application to decision making problems," IEEE Trans, on Systems, Man, and Cybernetics-A, vol. 31, no. 6, pp. 587-596,2001. [3] Z. Bubnicki, Uncertain Logics, Variables and Systems, Berlin: Springer Verlag, 2002. [4] J. Casillas et al. ), Interpretability Issues in Fuzzy Modeling, Berlin: Springer Verlag, 2003. [5] J. A. Dickerson and M. S. Lan, "Fuzzy rule extraction from numerical data for function approximation," IEEE Trans on System, Man, and CyberneticsB, vol.

7 . Then M has the same eigenvalues as Mi. -Y. Wang (a) (b) . . . : : : * * » « * * * . . 2: Dynamics of uncertainty: (a) Xx(k) with expanding supports, (b) X\(k) with converging supports, (c) the center of area of X\(k) for (a) and (b) (marked by "+" and "*", respectively. Chapter 2. 8892. Since one of the eigenvalues of M is outside of the unit circle, supp(X(fc)) will increase exponentially. 2(a), the initial conditions for all linguistic states are chosen as a triangle fuzzy number with parameter [left, center, right] = [1,2, 3].

Y. Wang mapping are constructed. 3, the structure, numerical procedure and existence of fixed-points of type-II LDS are discussed. 4, the LDS controller design principles for controlling type-II LDS are addressed. 5, the chapter is concluded with remarks for future works. 2 "type-I Linguistic Dynamic Systems The procedure of converting a conventional dynamic system into a type-I LDS is called abstracting process, namely, extracting linguistic dynamic models in words from conventional dynamic models in numbers.