Dominance on continuous Archimedean triangular norms and generalized Mulholland inequality

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Dominance on continuous Archimedean triangular norms and generalized Mulholland inequality

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Dominance on continuous Archimedean triangular norms and generalized Mulholland inequality

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

FUZZY SETS AND SYSTEMS

ISSN

0165-0114

e-ISSN

0165-0114

Svazek periodika

neuvedeno

Číslo periodika v rámci svazku

403

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

13

Strana od-do

88-100

Kód UT WoS článku

000589437700006

EID výsledku v databázi Scopus

2-s2.0-85078930215