algebra universalis

, Volume 53, Issue 1, pp 73–108 | Cite as

Many-valued relation algebras

Original Paper

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.

Mathematics Subject Classification (2000).

08A72 06D35 04A72 

Key words and phrases.

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

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Fundamentals of Computer Science, Faculty of MathematicsUniversity of BucharestBucharestRomania

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