A characterization of interval-valued residuated lattices

• Autores: B. Van Gasse, C. Cornelis, G. Deschrijver, E. Etienne Kerre
• Localización: International journal of approximate reasoning, ISSN 0888-613X, Vol. 49, Nº 2, 2008, págs. 478-487
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • As is well-known, residuated lattices (RLs) on the unit interval correspond to left-continuous t-norms. Thus far, a similar characterization has not been found for RLs on the set of intervals of [0, 1], or more generally, of a bounded lattice . In this paper, we show that the open problem can be solved if it is restricted, making only a few simple and intuitive assumptions, to the class of interval-valued residuated lattices (IVRLs).

    More specifically, we derive a full characterization of product and implication in IVRLs in terms of their counterparts on the base RL. To this aim, we use triangle algebras, a recently introduced variety of RLs that serves as an equational representation of IVRLs.