Download Crisp and Soft Computing with Hypercubical Calculus: New by Dr. Michael Zaus (auth.) PDF

By Dr. Michael Zaus (auth.)

Three transdisciplinary mainstreams of crisp and delicate computing are offered during this ebook. (1) a wholly new method of clinical modeling from scratch as in response to parity good judgment with new operators for binary computing and the recent framework of Langlet transforms. (2) A compact evaluation of the rules of fuzzy good judgment, and a finished remedy of fuzzy nonlinear dynamical predictor platforms when it comes to fuzzy cognitive maps. Readers drawn to new methods of causal modeling and nonlinear forecasting are brought to fuzzy wisdom engineering as a paradigm shift in clever computing. (3) New views for evolutionary computing with an integro-differential operator from parity common sense, and a scientific elaboration of autogenetic algorithms for seek in excessive dimensional function areas. Readers drawn to quick computing, useful purposes of causal reasoning with fuzzy good judgment, and interactive experimental keep an eye on environments as in accordance with evolutionary computing, will achieve major insights right into a number of computational strength tools.

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Extra info for Crisp and Soft Computing with Hypercubical Calculus: New Approaches to Modeling in Cognitive Science and Technology with Parity Logic, Fuzzy Logic, and Evolutionary Computing

Sample text

Jx, that is, the generalized XO R-reduction operator. By the same token, if =f. is subjected to the cumulative scan operator\, we get the derived function z +--=f. \x, that is, the generalized XOR-scan operator. 3 below. Notice that each operator has its dual operator by virtue of DeMorgan's laws 1 . 1 An extensive treatment of monadic (or unary) operators is provided by Iverson ([IVE62], [IVE78]) and Lochner ([LOC89]). Their scope of applications in science is discussed by Langlet ([LAN92a], [LAN93], [LAN94]) and Zaus ([ZA94], [ZA95b], [ZA95cJ) .

What remains is system inscrutability and lack of explanatory power. 1 Standard Function Systems It also shows the aforementioned isomorphism between time functions x(t) and Boolean functions f(x(t)). 1 are part of a far more general and universal system of standard functions. 2 . 2 prepares the reader for the binary counterpart of Fourier analysis. We take the cue from linear systems analysis according to which the Gaussian normal distribution N(O, 1) is the invariant of the Fourier transform.

3. 4. elements X E sn as vectorial representations of binary signals, the eXclusive-OR operation X$ y, defined on elements x, y E sn' the XOR operator EB~=l Xi E X E sn the binary scalar integral, the XOR operator EBf=l Xi E X E sn' the binary vector integral, I are systematically applied to signals x( t) regarding representations by spectra vs. representations by sequences in minute detail. This includes the dual relationship between spectra and pulses, signal transforms, and the algorithmic compression of binary signal representations and their transformations.

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