Dominance on continuous Archimedean triangular norms and generalized Mulholland inequality
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60460709%3A41310%2F21%3A85481" target="_blank" >RIV/60460709:41310/21:85481 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/abs/pii/S0165011419300806?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0165011419300806?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2020.01.012" target="_blank" >10.1016/j.fss.2020.01.012</a>
Alternative languages
Result language
angličtina
Original language name
Dominance on continuous Archimedean triangular norms and generalized Mulholland inequality
Original language description
As a preceding result, it has been shown that the dominance relation is not transitive on the set of strict triangular norms. This result has been achieved thanks to new results on Mulholland inequality. Recently, Saminger-Platz, De Baets, and De Meyer have introduced the generalized Mulholland inequality which characterizes the dominance on all continuous Archimedean triangular norms in an analogous way as does Mulholland inequality on the strict triangular norms. Based on these new results, the present paper shows that the dominance relation is not transitive on the set of nilpotent triangular norms and, consequently, on the set of continuous Archimedean triangular norms. This result is achieved by introducing a new sufficient condition under which a given function solves the generalized Mulholland inequality and by showing that the set of the functions that solve the inequality is not closed with respect to compositions.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
FUZZY SETS AND SYSTEMS
ISSN
0165-0114
e-ISSN
0165-0114
Volume of the periodical
neuvedeno
Issue of the periodical within the volume
403
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
13
Pages from-to
88-100
UT code for WoS article
000589437700006
EID of the result in the Scopus database
2-s2.0-85078930215