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Random Sets Unify, Explain, and Aid Known Uncertainty Methods in Expert Systems

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Book cover Random Sets

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 97))

Abstract

Numerous formalisms have been proposed for representing and processing uncertainty in expert systems. Several of these formalisms are somewhat ad hoc in the sense that some of their formulas seem to have been chosen rather arbitrarily.

In this paper, we show that random sets provide a natural general framework for describing uncertainty, a framework in which many existing formalisms appear as particular cases. This interpretation of known formalisms (e.g., of fuzzy logic) in terms of random sets enables us to justify many “ad hoc” formulas. In some cases, when several alternative formulas have been proposed, random sets help to choose the best ones (in some reasonable sense).

One of the main objectives of expert systems is not only to describe the current state of the world, but also to provide us with reasonable actions. The simplest case is when we have the exact objective function. In this case, random sets can help in choosing the proper method of “fuzzy optimization”.

As a test case, we describe the problem of choosing the best tests in technical diagnostics. For this problem, feasible algorithms are possible.

In many real-life situations, instead of an exact objective function, we have several participants with different objective functions, and we must somehow reconcile their (often conflicting) interests. Sometimes, standard approaches of game theory are not working. We show that in such situations, random sets present a working alternative. This is one of the cases when particular cases of random sets (such as fuzzy sets) are not sufficient, and general random sets are needed.

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Authors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso, El Paso, TX, 79968, USA

    Vladik Kreinovich

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  1. Vladik Kreinovich
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, The Johns Hopkins University, Baltimore, MD, 21218, USA

    John Goutsias

  2. Tactical Defense Systems, Lockheed Martin Corporation, Eagan, MN, 55121, USA

    Ronald P. S. Mahler

  3. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003, USA

    Hung T. Nguyen

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© 1997 Springer Science+Business Media New York

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Kreinovich, V. (1997). Random Sets Unify, Explain, and Aid Known Uncertainty Methods in Expert Systems. In: Goutsias, J., Mahler, R.P.S., Nguyen, H.T. (eds) Random Sets. The IMA Volumes in Mathematics and its Applications, vol 97. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1942-2_14

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  • DOI: https://doi.org/10.1007/978-1-4612-1942-2_14

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7350-9

  • Online ISBN: 978-1-4612-1942-2

  • eBook Packages: Springer Book Archive

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