Convex combinations of nilpotent triangular norms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F09%3A00157777" target="_blank" >RIV/68407700:21230/09:00157777 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Convex combinations of nilpotent triangular norms
Original language 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, Someobservations 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F07%2F1136" target="_blank" >GA201/07/1136: Mathematics of Uncertainty</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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