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Interval Type-2 Fuzzy Markov Chains

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Advances in Type-2 Fuzzy Sets and Systems

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 301))

Abstract

Uncertainties in fuzzy Markov chains can be treated in different ways. The use of interval type-2 fuzzy sets (IT2FS) allows describing the distributional behavior of an uncertain discrete-time Markov process through infinite type-1 fuzzy sets embedded in its Footprint of Uncertainty. In this way, a finite state fuzzy Markov chain process is defined in an interval type-2 fuzzy environment. To do so, its limiting properties and its type-reduced behavior are defined and applied to two explanatory examples.

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Notes

  1. 1.

    As a function of the \(i_{th}\) state e.g. \(x(i)\).

  2. 2.

    This matrix is also known as the Fuzzy Distribution of \(x\).

  3. 3.

    Here, \(\oint \) denotes crisp integration.

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Authors and Affiliations

  1. Universidad Distrital Francisco José de Caldas, Bogotá, Colombia

    Juan Carlos Figueroa-García

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  1. Juan Carlos Figueroa-García
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Correspondence to Juan Carlos Figueroa-García .

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Editors and Affiliations

  1. Ryerson University, Victoria Street 350, Toronto, M5B 2K3, Ontario, Canada

    Alireza Sadeghian

  2. Hughes Aircraft Electrical Engineering B, Department of Electrical Engineering - S, University of Southern California, 3740 McClintock Ave., Los Angeles, 90089-2564, California, USA

    Jerry M. Mendel

  3. Ryerson University, Victoria Street 350, Toronto, M5B 2K3, Ontario, Canada

    Hooman Tahayori

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Figueroa-García, J.C. (2013). Interval Type-2 Fuzzy Markov Chains. In: Sadeghian, A., Mendel, J., Tahayori, H. (eds) Advances in Type-2 Fuzzy Sets and Systems. Studies in Fuzziness and Soft Computing, vol 301. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6666-6_4

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  • DOI: https://doi.org/10.1007/978-1-4614-6666-6_4

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