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H J Zimmermann - One of the best experts on this subject based on the ideXlab platform.

  • fuzzy Set Theory
    Wiley Interdisciplinary Reviews: Computational Statistics, 2010
    Co-Authors: H J Zimmermann
    Abstract:

    Since its inception in 1965, the Theory of fuzzy Sets has advanced in a variety of ways and in many disciplines. Applications of this Theory can be found, for example, in artificial intelligence, computer science, medicine, control engineering, decision Theory, expert systems, logic, management science, operations research, pattern recognition, and robotics. Mathematical developments have advanced to a very high standard and are still forthcoming to day. In this review, the basic mathematical framework of fuzzy Set Theory will be described, as well as the most important applications of this Theory to other theories and techniques. Since 1992 fuzzy Set Theory, the Theory of neural nets and the area of evolutionary programming have become known under the name of ‘computational intelligence’ or ‘soft computing’. The relationship between these areas has naturally become particularly close. In this review, however, we will focus primarily on fuzzy Set Theory. Applications of fuzzy Set Theory to real problems are abound. Some references will be given. To describe even a part of them would certainly exceed the scope of this review. Copyright © 2010 John Wiley & Sons, Inc. For further resources related to this article, please visit the WIREs website.

Kazushige Terui - One of the best experts on this subject based on the ideXlab platform.

  • Light Affine Set Theory: A Naive Set Theory of Polynomial Time
    Studia Logica, 2004
    Co-Authors: Kazushige Terui
    Abstract:

    In [7], a naive Set Theory is introduced based on a polynomial time logical system, Light Linear Logic ( LLL ). Although it is reasonably claimed that the Set Theory inherits the intrinsically polytime character from the underlying logic LLL , the discussion there is largely informal, and a formal justification of the claim is not provided sufficiently. Moreover, the syntax is quite complicated in that it is based on a non-traditional hybrid sequent calculus which is required for formulating LLL . In this paper, we consider a naive Set Theory based on Intuitionistic Light Affine Logic ( ILAL ), a simplification of LLL introduced by [1], and call it Light Affine Set Theory ( LAST ). The simplicity of LAST allows us to rigorously verify its polytime character. In particular, we prove that a function over {0, 1}* is computable in polynomial time if and only if it is provably total in LAST .

  • Light Affine Set Theory: A Naive Set Theory of Polynomial Time
    Studia Logica, 2004
    Co-Authors: Kazushige Terui
    Abstract:

    In [7], a naive Set Theory is introduced based on a polynomial time logical system, Light Linear Logic (LLL). Although it is reasonably claimed that the Set Theory inherits the intrinsically polytime character from the underlying logic LLL, the discussion there is largely informal, and a formal justification of the claim is not provided sufficiently. Moreover, the syntax is quite complicated in that it is based on a non-traditional hybrid sequent calculus which is required for formulating LLL.

W Lodwick - One of the best experts on this subject based on the ideXlab platform.

  • Interval analysis and fuzzy Set Theory
    Fuzzy Sets and Systems, 2003
    Co-Authors: Ramon Moore, W Lodwick
    Abstract:

    An overview of interval analysis, its development and its relationship to fuzzy Set Theory was presented. The levels of possibility over the intervals resulting from interval computation with the interval parameters was determined by utilizing the properties of possibility distributions assumed by fuzzy Set Theory. The interval analysis and fuzzy Set Theory as areas of active research in mathematics, numerical analysis and computer science was highlighted.

Ramon Moore - One of the best experts on this subject based on the ideXlab platform.

  • Interval analysis and fuzzy Set Theory
    Fuzzy Sets and Systems, 2003
    Co-Authors: Ramon Moore, W Lodwick
    Abstract:

    An overview of interval analysis, its development and its relationship to fuzzy Set Theory was presented. The levels of possibility over the intervals resulting from interval computation with the interval parameters was determined by utilizing the properties of possibility distributions assumed by fuzzy Set Theory. The interval analysis and fuzzy Set Theory as areas of active research in mathematics, numerical analysis and computer science was highlighted.

Benjamin Naumann - One of the best experts on this subject based on the ideXlab platform.

  • Classical Descriptive Set Theory
    2020
    Co-Authors: Benjamin Naumann
    Abstract:

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