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Several extensions of truth values in fuzzy logic

  • Masao Mukaidono
Communications 3B Logics for AI
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1609)

Abstract

Truth values in fuzzy logic are extended into interval truth values {[a, b]: 0≤ab≤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 ab 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), (xy), 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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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Masao Mukaidono
    • 1
  1. 1.Department of Computer ScienceMeiji UniversityKawasaki-shiJapan

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