An Algebraic Approach to Propositional Fuzzy Logic
Journal of Logic, Language and Information
A note to the definition of the ŁΠ-algebras
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Barycentric Algebras and Gene Expression
WILF '09 Proceedings of the 8th International Workshop on Fuzzy Logic and Applications
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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 LΠ-algebra, the algebra of Łukasiewicz 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.