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Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy Uncertainty

Author

Listed:
  • Vladik Kreinovich

    (Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA
    These authors contributed equally to this work.)

  • Olga Kosheleva

    (Department of Teacher Education, University of Texas at El Paso, El Paso, TX 79968, USA
    These authors contributed equally to this work.)

  • Patricia Melin

    (Division of Graduate Studies and Research, Tijuana Institute of Technology, Tomas Aquino, Tijuana 22685, Baja California, Mexico
    These authors contributed equally to this work.)

  • Oscar Castillo

    (Division of Graduate Studies and Research, Tijuana Institute of Technology, Tomas Aquino, Tijuana 22685, Baja California, Mexico
    These authors contributed equally to this work.)

Abstract

It is known that, to more adequately describe expert knowledge, it is necessary to go from the traditional (type-1) fuzzy techniques to higher-order ones: type-2, probably type-3 and even higher. Until recently, only type-1 and type-2 fuzzy sets were used in practical applications. However, lately, it turned out that type-3 fuzzy sets are also useful in some applications. Because of this practical importance, it is necessary to design efficient algorithms for data processing under such type-3 (and higher-order) fuzzy uncertainty. In this paper, we show how we can combine known efficient algorithms for processing type-1 and type-2 uncertainty to come up with a new algorithm for the type-3 case.

Suggested Citation

  • Vladik Kreinovich & Olga Kosheleva & Patricia Melin & Oscar Castillo, 2022. "Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy Uncertainty," Mathematics, MDPI, vol. 10(13), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2361-:d:856328
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    References listed on IDEAS

    as
    1. Tao Zhao & Zhenbo Wei, 2016. "On Characterization of Rough Type-2 Fuzzy Sets," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-13, February.
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