A map characterizing the fuzzy points and columns of a T-indistinguishability operator

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dc.contributor	Universitat Politècnica de Catalunya. Departament d'Estructures a l'Arquitectura
dc.contributor	Universitat Politècnica de Catalunya. FIA - Modelització Matemàtica Funcional i Aplicacions
dc.contributor.author	Boixader Ibáñez, Dionís
dc.contributor.author	Recasens Ferrés, Jorge
dc.date	2005-10
dc.identifier.citation	10.1142/S0218488508005108
dc.identifier.uri	http://hdl.handle.net/2117/1178
dc.language.iso	eng
dc.relation	http://www.worldscientific.com/doi/abs/10.1142/S0218488508005108
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Expert systems (Computer sciences)
dc.subject	Fuzzy systems
dc.subject	Artificial intelligence
dc.subject	Fuzzy logic
dc.subject	Fuzzy sets
dc.subject	Fuzzy point
dc.subject	Fuzzy relation
dc.subject	Column of a fuzzy relation
dc.subject	T-norm
dc.subject	T-indistinguishability operator
dc.subject	Generator
dc.subject	Sistemes experts (Informàtica)
dc.subject	Sistemes difusos
dc.subject	Intel·ligència artificial
dc.subject	Lògica difusa
dc.subject	Conjunts difusos
dc.subject	Classificació AMS::03 Mathematical logic and foundations::03E Set theory
dc.subject	Classificació AMS::68 Computer science::68T Artificial intelligence
dc.title	A map characterizing the fuzzy points and columns of a T-indistinguishability operator
dc.type	info:eu-repo/semantics/article
dc.description.abstract	A new map (ΛE) between fuzzy subsets of a universe X endowed with a T-indistinguishability operator E is introduced. The main feature of ΛE is that it has the columns of E as fixed points, and thus it provides us with a new criterion to decide whether a generator is a column. Two well known maps (φE and ψE) are also reviewed, in order to compare them with ΛE. Interesting properties of the fixed points of ΛE and Λ2 E are studied. Among others, the fixed points of ΛE (Fix(ΛE)) are proved to be the maximal fuzzy points of (X,E) and the fixed points of Λ2 E coincide with the Image of ΛE. An isometric embedding of X into Fix(ΛE) is established and studied.

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