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

By Dr. Michael Zaus (auth.)

Three transdisciplinary mainstreams of crisp and gentle computing are awarded during this e-book. (1) a completely new method of medical modeling from scratch as in keeping with parity common sense with new operators for binary computing and the hot framework of Langlet transforms. (2) A compact assessment of the rules of fuzzy common sense, and a finished therapy of fuzzy nonlinear dynamical predictor platforms by way of fuzzy cognitive maps. Readers attracted 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 speedy computing, useful purposes of causal reasoning with fuzzy good judgment, and interactive experimental keep watch over environments as in response to evolutionary computing, will achieve major insights right into a number of computational strength tools.

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Extra resources 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

2 . The point is that if standard function systems can be obtained from parity integration alone, then it should be possible to obtain the binary Taylor derivatives just as well from parity integration with maximal computational efficacy. That the analytical approach can be compressed into a single operator will be demonstrated now by using the operator ffii=I Xi E x E Bn. We show this again in minute detail, since otherwise the reader won't appreciate the power of parity integration. 6 summarizes how we obtain the sequence of binary vector viz.

From Bi ( t) to Bi+l ( t). 2). e. 1 Standard Function Systems assigned a unique value of each Ai or Bi. By increasing the index i, the length of single "pulses" or "pauses" decreases increasingly whereby the underlying quantization depends on the shortest eigentime Tmin of a particular system. Theoretically, this implies a maximal index m for signals regarding natural or artificial systems such that the functions Am(t) viz. Bm(t) take the possibly fastest changes of a system into account. If we consider the half-period of Am(t) or Bm(t) as a time-quantum, then the duration of this time-quantum is given by the inequality TQ ~ To·2-(m+I).

4 Motions, Inner Products, and Genitons Pascal's triangle modulo 2 and its completion to Pascal's square on the one hand, and the group of motions regarding binary parity matrices on the other hand will play a central role in later chapters. The same holds for inner products involving XOR. This chapter provides therefore a brief survey of some standard concepts and computational aspects. 2 . 4 Motions, Inner Products, and the Geniton 29 the complement-preservation property of motions. The two most important kinds of motions will be rotations of vectors and reflections of arrays in Bn for effective transforms and the group of transformation operators.

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