Kolmogorov’s Theorem and Its Impact on Soft Computing

Hung T. Nguyen () and Vladik Kreinovich ()
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Hung T. Nguyen: New Mexico State University, Department of Mathematical Sciences
Vladik Kreinovich: University of Texas at El Paso, Department of Computer Science

A chapter in The Ordered Weighted Averaging Operators, 1997, pp 3-17 from Springer

Abstract: Abstract In this chapter, we describe various applications of the Kolmogorov’s theorem on representing continuous functions of several variables (as superpositions of functions of one and two variables) to soft computing. Kolmogorov’s theorem leads to a theoretical justification, as well as to design methodologies, for neural networks. In the design of intelligent systems, Kolmogorov’s theorem is used to show that general logical operators can be expressed in terms of basic fuzzy logic operations. In the area of reliable computing (i.e., computing that takes into consideration the accuracy of the input data), an extended version of Kolmogorov’s theorem justifies the need to use operations with three or more operands in soft computing. Such operations have already been actively used in soft computing; the simplest (and, so far, most used) of such operations are ordered weighted averaging (OWA) operators proposed by R. R. Yager.

Keywords: Neural networks; soft computing; Kolmogorov’s theorem; reliable (and interval) computing; fuzzy logic; logical operations (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-6123-1_1

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DOI: 10.1007/978-1-4615-6123-1_1

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