Some algebraic theory for many-valued relation algebras

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.

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Correspondence to Andrei Popescu.

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Dedicated to my Professor, George Georgescu.

Received September 22, 2005; accepted in final form January 20, 2006.

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Popescu, A. Some algebraic theory for many-valued relation algebras. Algebra univers. 56, 211–235 (2007). https://doi.org/10.1007/s00012-007-1995-3

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2000 Mathematics Subject Classification:

  • 03G15
  • 06D35
  • 03B52

Keywords and phrases:

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