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35 Years of Fuzzy Set Theory pp 57–82Cite as

Interval-Valued Algebras and Fuzzy Logics

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 261))

Abstract

In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000, Gent, Belgium

    Bart Van Gasse, Chris Cornelis & Glad Deschrijver

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  1. Bart Van Gasse
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  2. Chris Cornelis
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  3. Glad Deschrijver
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Editors and Affiliations

  1. Ghent University, Gent, Belgium

    Chris Cornelis , Glad Deschrijver , Mike Nachtegael , Steven Schockaert  & Yun Shi , , ,  & 

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Van Gasse, B., Cornelis, C., Deschrijver, G. (2010). Interval-Valued Algebras and Fuzzy Logics. In: Cornelis, C., Deschrijver, G., Nachtegael, M., Schockaert, S., Shi, Y. (eds) 35 Years of Fuzzy Set Theory. Studies in Fuzziness and Soft Computing, vol 261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16629-7_4

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  • DOI: https://doi.org/10.1007/978-3-642-16629-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16628-0

  • Online ISBN: 978-3-642-16629-7

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