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Algebraic study of axiomatic extensions of triangular norm based fuzzy logics


Algebraic study of axiomatic extensions of triangular norm based fuzzy logics
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

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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

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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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Bibliographic information

Physical Description : XVI, 192 p. : gráf. ; 24 cm

ISBN: 978-84-00-08538-4

Publication: Bellaterra (España) : Consejo Superior de Investigaciones Científicas, 2007

Reference CSIC: 11474

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