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Statements

Subject Item
n2:RIV%2F68407700%3A21230%2F09%3A00157777%21RIV10-GA0-21230___
rdf:type
skos:Concept n15:Vysledek
dcterms: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.
dcterms:title
Convex combinations of nilpotent triangular norms Convex combinations of nilpotent triangular norms
skos:prefLabel
Convex combinations of nilpotent triangular norms Convex combinations of nilpotent triangular norms
skos:notation
RIV/68407700:21230/09:00157777!RIV10-GA0-21230___
n4:aktivita
n17:P
n4:aktivity
P(GA201/07/1136)
n4:cisloPeriodika
1
n4:dodaniDat
n7:2010
n4:domaciTvurceVysledku
n10:3187608
n4:druhVysledku
n6:J
n4:duvernostUdaju
n11:S
n4:entitaPredkladatele
n14:predkladatel
n4:idSjednocenehoVysledku
308313
n4:idVysledku
RIV/68407700:21230/09:00157777
n4:jazykVysledku
n13:eng
n4:klicovaSlova
Nilpotent triangular norm; Reidmeister condition; Convex combination
n4:klicoveSlovo
n9:Nilpotent%20triangular%20norm n9:Reidmeister%20condition n9:Convex%20combination
n4:kodStatuVydavatele
US - Spojené státy americké
n4:kontrolniKodProRIV
[CAD7E3777247]
n4:nazevZdroje
Journal of Mathematical Analysis and Its Applications
n4:obor
n5:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
2
n4:projekt
n18:GA201%2F07%2F1136
n4:rokUplatneniVysledku
n7:2009
n4:svazekPeriodika
350
n4:tvurceVysledku
Petrík, Milan
n4:wos
000261895800025
s:issn
0022-247X
s:numberOfPages
5
n16:organizacniJednotka
21230