论文信息 - The Archimedean property for t-norms in interval-valued fuzzy set theory

The Archimedean property for t-norms in interval-valued fuzzy set theory

Abstract In this paper, the Archimedean property of t-norms on the lattice L I is introduced, where L I is the underlying lattice of interval-valued fuzzy set theory [R. Sambuc, Fonctions Φ -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)]. Two additional variations on this property are also introduced: weakly and strong Archimedean property. We investigate the relationship with the (weak) limit property and obtain several necessary and sufficient conditions for a t-norm on L I to be Archimedean. We discuss the Archimedean property for special classes of t-norms on L I based on t-norms on the unit interval.

Glad Deschrijver | G. Deschrijver

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