Arithmetic operators in interval-valued fuzzy set theory

  • Authors:

  • Glad Deschrijver

  • Affiliations:

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

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

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Abstract

We introduce the addition, subtraction, multiplication and division on L^I, where L^I is the underlying lattice of both interval-valued fuzzy set theory [R. Sambuc, Fonctions @F-floues. Application a l'aide au diagnostic en pathologie thyroidienne, Ph.D. Thesis, Universite de Marseille, France, 1975] and intuitionistic fuzzy set theory [K.T. Atanassov, Intuitionistic fuzzy sets, 1983, VII ITKR's Session, Sofia (deposed in Central Sci. Technical Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian)]. We investigate some algebraic properties of these operators. We show that using these operators the pseudo-t-representable extensions of the Lukasiewicz t-norm and the product t-norm on the unit interval to L^I and some related operators can be written in a similar way as their counterparts on ([0,1],=