By Derong Liu, Fei-Yue Wang

ISBN-10: 9812567348

ISBN-13: 9789812567345

ISBN-10: 9812773924

ISBN-13: 9789812773920

Computational Intelligence (CI) is a lately rising quarter in primary and utilized examine, exploiting a few complicated details processing applied sciences that normally include 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 coffee resolution expense, it turns into glaring that composing tools of CI will be operating simultaneously instead of individually. it truly is this conviction that examine at the synergism of CI paradigms has skilled major progress within the final decade with a few parts nearing adulthood whereas many others closing unresolved. This ebook systematically summarizes the newest findings and sheds gentle at the respective fields that would bring about destiny breakthroughs.

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**Example text**

Observe that the support of X\ (k) expands to the size of the order of 109 in 29 iterations in this case, however, the center of area of X\{k) is still equal to x\ (k) no matter how big and how fast the supports grow. This example indicates that the uncertainty of the initial condition grows exponentially for a stable linear system. Is this a general case? To address this question, let us analyze the evolving processes of supports of linguistic states. For a fuzzy number X, let us use supp(X) to denote the size of its support.

However, in general it is difficult to study the behaviors of type-I LDS analytically. In this chapter, we present a numerical method called a-cut mapping to study type-I LDS. Their second method of generating fuzzy dynamic systems is to use fuzzy compositions. In this case, the corresponding fuzzy dynamic systems are a special case of typeII LDS of which the evolving laws are represented by fuzzy relational matrices. An energetic function was introduced in [9] to study the stability of this kind of type-II LDS and later its controllability [5].

17] W Pedrycz, "Fuzzy neural networks and neurocomputations," Fuzzy Sets and Systems, vol. 56, pp. 1-28,1993. [18] W Pedrycz and A. Rocha, "Knowledge-based neural networks," IEEE Trans, on Fuzzy Systems, vol. 1, pp. 254-266,1993. Chapter 1. A Quest for Granular Computing and Logic Processing [19] W. Pedrycz, P. Lam, and A. F. Rocha, "Distributed fuzzy modelling," IEEE Trans, on Systems, Man and Cybernetics-B, vol. 5, pp. 769-780,1995. [20] W. Pedrycz and F. Gomide, An Introduction to Fuzzy Sets: Analysis and Design, Boston: MIT Press, 1998.

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