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Kolmogorov’s Theorem and Its Impact on Soft Computing

In: The Ordered Weighted Averaging Operators

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Listed:
  • Hung T. Nguyen

    (New Mexico State University, Department of Mathematical Sciences)

  • Vladik Kreinovich

    (University of Texas at El Paso, Department of Computer Science)

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.

Suggested Citation

  • Hung T. Nguyen & Vladik Kreinovich, 1997. "Kolmogorov’s Theorem and Its Impact on Soft Computing," Springer Books, in: Ronald R. Yager & Janusz Kacprzyk (ed.), The Ordered Weighted Averaging Operators, pages 3-17, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-6123-1_1
    DOI: 10.1007/978-1-4615-6123-1_1
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