Some characterizations of T-power based implications

Recently, the so-called family of T-power based implications was introduced. These operators involve the use of Zadeh’s quantifiers based on powers of t-norms in its definition. Due to the fact that Zadeh’s quantifiers constitute the usual method to modify fuzzy propositions, this family of fuzzy im...

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Detalles Bibliográficos
Autores: Massanet, Sebastià, Recasens Ferrés, Jorge|||0000-0003-2304-0032, Torrens Serra, Joan
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/132787
Acceso en línea:https://hdl.handle.net/2117/132787
https://dx.doi.org/10.1016/j.fss.2018.08.007
Access Level:acceso abierto
Palabra clave:Fuzzy logic
Fuzzy implication function
T-power based implications
Invariance property
continuous t-norm
powers of t-norms
Lògica difusa
Àrees temàtiques de la UPC::Matemàtiques i estadística::Lògica matemàtica
Descripción
Sumario:Recently, the so-called family of T-power based implications was introduced. These operators involve the use of Zadeh’s quantifiers based on powers of t-norms in its definition. Due to the fact that Zadeh’s quantifiers constitute the usual method to modify fuzzy propositions, this family of fuzzy implication functions satisfies an important property in approximate reasoning such as the invariance of the truth value of the fuzzy conditional when both the antecedent and the consequent are modified using the same quantifier. In this paper, an in-depth analysis of this property is performed by characterizing all binary functions satisfying it. From this general result, a fully characterization of the family of T-power based implications is presented. Furthermore, a second characterization is also proved in which surprisingly the invariance property is not explicitly used.