Algebraic study of axiomatic extensions of triangular norm based fuzzy logics

Carles Noguera i Clofent Affiliation: Consejo Superior de Investigaciones Científicas. Institut d'Investigació en Intel-ligencia Artificial (Bellaterra, España) Biography: Not available Close window

Carles Noguera i Clofent About the authors  Publication year: 2007 Language: English Subjects: Science and Technology Collection: Monografies de l'Institut d'Investigació en Intel-ligencia Artificial Free eBook

Abstract:

According to the Zadeh’s famous distinction, Fuzzy Logic in narrow sense, as opposed to Fuzzy Logic in broad sense, is the study of logical systems aiming at a formalization of approximate reasoning. In the systems commonly used the strong conjunction connective is interpreted by a triangular norm (t-norm, for short) while the implication connective is interpreted by its residuum. Therefore, the usual logical systems for Fuzzy Logic are based on t-norms with a residuum. The necessary and sufficient condition for a t-norm to have a residuum is the left-continuity. In order to define the based t-norm based fuzzy logic, Esteva and Godo introduced the system MTL, which was indeed proved to be complete with respect to the semantics given by all left-continuous t-norms and their residua.

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