Abstract Barycentric Algebras

• Autorzy: Romanowska A.B. , Smith J.D.H. , Orłowska E.
• Języki publikacji: EN

Abstrakty

EN

This paper presents a new approach to the study of (real) barycentric algebras, in particular convex subsets of real affine spaces. Barycentric algebras are cast in the setting of two-sorted algebras. The real unit interval indexing the set of basic operations of a barycentric algebra is replaced by an LP-algebra, the algebra of ukasiewicz Product Logic. This allows one to define barycentric algebras abstractly, independently of the choice of the unit real interval. It reveals an unexpected connection between barycentric algebras and (fuzzy) logic. The new class of abstract barycentric algebras incorporates barycentric algebras over any linearly ordered field, the B-sets of G. M. Bergman, and E. G. Manes' if-then-else algebras over Boolean algebras.

Słowa kluczowe

EN

affine space; barycentric algebra; mode; cancellavity mode; LII-algebra; Łukaszewicz Product Logic; heterogeneous algebra; if-then-else algebra; rectangular algebra

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2007
• Tom: Vol. 81, nr 1-3
• Strony: 257--273
• Opis fizyczny: bibliogr. 32 poz.

Twórcy

autor

Romanowska A.B.

autor

Smith J.D.H.

autor

Orłowska E.

• Warsaw University of Technology, 00-661 Warsaw, Poland,

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