Many-valued relation algebras


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.

This is a preview of subscription content, access via your institution.

Author information



Corresponding author

Correspondence to Andrei Popescu.

Additional information

Dedicated to the Memory of Wim Blok

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

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Popescu, A. Many-valued relation algebras. Algebra univers. 53, 73–108 (2005).

Download citation

Mathematics Subject Classification (2000).

  • 08A72
  • 06D35
  • 04A72

Key words and phrases.

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