About: Convex combinations of nilpotent triangular norms

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper we deal with the open problem of convex combinations of continuous triangular norms stated by Alsina, Frank, and Schweizer [C. Alsina, M.J. Frank, B. Schweizer, Problems on associative functions, Aequationes Math. 66 (2003) 128--140, Problems 5 and 6]. They pose a question whether a non-trivial convex combination of triangular norms can ever be a triangular norm. The main result of this paper gives a negative answer to the question for any pair of continuous Archimedean triangular norms with different supports. With the help of this result we show that a non-trivial convex combination of nilpotent t-norms is never a t-norm. The main result also gives an alternative proof to the result presented by Ouyang and Fang [Y. Ouyang, J. Fang, Some observations about the convex combination of continuous triangular norms, Nonlinear Anal., 68 (11) (2008) 3382--3387, Theorem 3.1]. In proof of the main theorem we utilize the Reidmeister condition known from the web geometry. In this paper we deal with the open problem of convex combinations of continuous triangular norms stated by Alsina, Frank, and Schweizer [C. Alsina, M.J. Frank, B. Schweizer, Problems on associative functions, Aequationes Math. 66 (2003) 128--140, Problems 5 and 6]. They pose a question whether a non-trivial convex combination of triangular norms can ever be a triangular norm. The main result of this paper gives a negative answer to the question for any pair of continuous Archimedean triangular norms with different supports. With the help of this result we show that a non-trivial convex combination of nilpotent t-norms is never a t-norm. The main result also gives an alternative proof to the result presented by Ouyang and Fang [Y. Ouyang, J. Fang, Some observations about the convex combination of continuous triangular norms, Nonlinear Anal., 68 (11) (2008) 3382--3387, Theorem 3.1]. In proof of the main theorem we utilize the Reidmeister condition known from the web geometry. (en)
Title	Convex combinations of nilpotent triangular norms Convex combinations of nilpotent triangular norms (en)
skos:prefLabel	Convex combinations of nilpotent triangular norms Convex combinations of nilpotent triangular norms (en)
skos:notation	RIV/68407700:21230/09:00157777!RIV10-GA0-21230___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GA201/07/1136)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Petrík, Milan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	308313
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/09:00157777
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Nilpotent triangular norm; Reidmeister condition; Convex combination (en)
http://linked.open.../riv/klicoveSlovo	Convex combination Nilpotent triangular norm Reidmeister condition
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[CAD7E3777247]
http://linked.open...i/riv/nazevZdroje	Journal of Mathematical Analysis and Its Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Mathematics of Uncertainty
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	350
http://linked.open...iv/tvurceVysledku	Petrík, Milan
http://linked.open...ain/vavai/riv/wos	000261895800025
issn	0022-247X
number of pages	5 (xsd:int)
http://localhost/t...ganizacniJednotka	21230
is http://linked.open...avai/riv/vysledek of	Convex combinations of nilpotent triangular norms Convex combinations of nilpotent triangular norms Convex combinations of nilpotent triangular norms Convex combinations of nilpotent triangular norms

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