Generalized arithmetic operators and their relationship to t-norms in interval-valued fuzzy set theory

  • Authors:

  • Glad Deschrijver

  • Affiliations:

  • Fuzziness and Uncertainty Modelling Research Unit, Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B--9000 Gent, Belgium

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2009

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Abstract

In this paper we study extensions of the arithmetic operators +, -, ., @? to the lattice L^I of closed subintervals of the unit interval. Starting from a minimal set of axioms that these operators must fulfill, we investigate which properties they satisfy. We also investigate some classes of t-norms on L^I which can be generated using these operators; these classes provide natural extensions of the Lukasiewicz, product, Frank, Schweizer-Sklar and Yager t-norms to L^I.