Many-valued relation algebras

Abstract.

We introduce MV-relation algebras (MVRAs) and distributive MV-relation algebras (DMVRAs), many-valued generalizations of classical relation algebras and study some of their arithmetical properties. We provide corresponding notions of group relation algebra and complex algebra and generalize some results about them from the classical case. For this, we work with more general structures than MVRAs and DMVRAs, by replacing the MV part with a BL-algebra, obtaining what we call fuzzy relation algebras and distributive fuzzy relation algebras.

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Correspondence to Andrei Popescu.

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Dedicated to the Memory of Wim Blok

Received February 12, 2003; accepted in final form October 15, 2004.

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Popescu, A. Many-valued relation algebras. Algebra univers. 53, 73–108 (2005). https://doi.org/10.1007/s00012-005-1916-2

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Mathematics Subject Classification (2000).

  • 08A72
  • 06D35
  • 04A72

Key words and phrases.

  • many-valued and fuzzy relation algebra
  • MV-algebra
  • BL-algebra
  • continuous t-norm