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Several extensions of truth values in fuzzy logic

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Foundations of Intelligent Systems (ISMIS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1609))

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Abstract

Truth values in fuzzy logic are extended into interval truth values {[a, b]: 0≤a≤b≤1} from the numerical truth values of [0, 1]. Next we extend this interval truth values into two directions; one is to n-dimensional case such as [a 1,...,a n ] where a 1≤...≤a n , and the other is to dropping the condition a≤b in [a, b]. We examine the algebraic structures of these truth values on which three kinds of logic operations AND(·), OR(∨), NOT(⊃ are defined, where we interpret (x·y), (x∨y), 0 and (⊃x) as min(x, y), max(x, y), and (1−x), respectively. It is shown that we can find out structures of Kleene algebra and De Morgan algebra in these truth values.

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Authors and Affiliations

  1. Department of Computer Science, Meiji University, 1-1-1 Higashi-mita, Tama-ku, 214-8571, Kawasaki-shi, Japan

    Masao Mukaidono

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  1. Masao Mukaidono
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Zbigniew W. Raś Andrzej Skowron

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© 1999 Springer-Verlag Berlin Heidelberg

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Mukaidono, M. (1999). Several extensions of truth values in fuzzy logic. In: Raś, Z.W., Skowron, A. (eds) Foundations of Intelligent Systems. ISMIS 1999. Lecture Notes in Computer Science, vol 1609. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0095114

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  • DOI: https://doi.org/10.1007/BFb0095114

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65965-5

  • Online ISBN: 978-3-540-48828-6

  • eBook Packages: Springer Book Archive

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