Associated with any [0,1]-valued propositional logic with a complete algebraic semantics, one can consider algebras of families of fuzzy sets over a classical universe, endowed with the appropriate operations. For the three most important schematic extensions of Hájek’s Basic (Fuzzy) Logic, we investigate the existence and the structure of such algebras of fuzzy sets in the corresponding algebraic varieties. In the general case of Basic Logic itself, and in sharp contrast to the three aforementioned extensions, we show that there actually exist different, incomparable notions of algebras of fuzzy sets.
Algebras of Fuzzy Sets in Logics based on Continuous Triangular Norms / S. Aguzzoli, B. Gerla, V. Marra - In: Symbolic and Quantitative Approaches to Reasoning with Uncertainty : 10th European Conference, ECSQARU 2009, Verona, Italy, July 1-3, 2009 : Proceedings / [a cura di] C. Sossai, G. Chemello. - Berlin : Springer, 2009. - ISBN 9783642029059. - pp. 875-886 (( Intervento presentato al 10. convegno ECSQARU 2009 tenutosi a Verona, Italy nel 2009.
Algebras of Fuzzy Sets in Logics based on Continuous Triangular Norms
S. AguzzoliPrimo
;V. MarraUltimo
2009
Abstract
Associated with any [0,1]-valued propositional logic with a complete algebraic semantics, one can consider algebras of families of fuzzy sets over a classical universe, endowed with the appropriate operations. For the three most important schematic extensions of Hájek’s Basic (Fuzzy) Logic, we investigate the existence and the structure of such algebras of fuzzy sets in the corresponding algebraic varieties. In the general case of Basic Logic itself, and in sharp contrast to the three aforementioned extensions, we show that there actually exist different, incomparable notions of algebras of fuzzy sets.
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