Algebra universalis

, Volume 56, Issue 2, pp 211–235

Some algebraic theory for many-valued relation algebras

Article

DOI: 10.1007/s00012-007-1995-3

Cite this article as:
Popescu, A. Algebra univers. (2007) 56: 211. doi:10.1007/s00012-007-1995-3

Abstract.

We study MV-relation-algebras, appearing by abstracting away from the concrete many-valued relations and the operations on them, such as composition and converse. MV-relation-algebras are MV generalizations of the relation algebras developed by A. Tarski and his school starting from the late forties. Some facts about ideals, congruences, and various types of elements are proved. A characterization of the “natural” MV-relation-algebras (a parameterized analogue of the classical full proper relation algebras) is also provided, as well as a first-order elementary description of matrix MV-relation algebras.

2000 Mathematics Subject Classification:

03G15 06D35 03B52 

Keywords and phrases:

MV-relation-algebra many-valued (fuzzy) relation MV-algebra 

Copyright information

© Birkhäuser Verlag, Basel 2007

Authors and Affiliations

  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania
  2. 2.Fundamentals of Computer Science, Faculty of MathematicsUniversity of BucharestBucharestRomania
  3. 3.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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