Generation of continuous T-norms through latticial operations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2402I2V" target="_blank" >RIV/61988987:17610/23:A2402I2V - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S016501142200392X" target="_blank" >https://www.sciencedirect.com/science/article/pii/S016501142200392X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2022.09.005" target="_blank" >10.1016/j.fss.2022.09.005</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Generation of continuous T-norms through latticial operations

Popis výsledku v původním jazyce

It is well known that the usual point-wise ordering over the set of t-norms makes it a poset but not a lattice, i.e., the point-wise maximum or minimum of two t-norms need not always be a t-norm again. In this work, we propose, two binary operations on the set of continuous Archimedean t-norms and obtain, via these binary operations, a partial order relation ⊑, different from the usual point-wise order ≤, on the set . As an interesting outcome of this structure, some stronger versions of some existing results dealing with the upper and lower bounds of two continuous Archimedean t-norms with respect to the point-wise order ≤ are also obtained. Finally, with the help of the operations on the set , two binary operations on the set of continuous t-norms are proposed and showed that the discussed structure is a lattice. Thus we have both a way of generating continuous t-norms from continuous t-norms and also obtain an order on them.

Název v anglickém jazyce

Generation of continuous T-norms through latticial operations

Popis výsledku anglicky

It is well known that the usual point-wise ordering over the set of t-norms makes it a poset but not a lattice, i.e., the point-wise maximum or minimum of two t-norms need not always be a t-norm again. In this work, we propose, two binary operations on the set of continuous Archimedean t-norms and obtain, via these binary operations, a partial order relation ⊑, different from the usual point-wise order ≤, on the set . As an interesting outcome of this structure, some stronger versions of some existing results dealing with the upper and lower bounds of two continuous Archimedean t-norms with respect to the point-wise order ≤ are also obtained. Finally, with the help of the operations on the set , two binary operations on the set of continuous t-norms are proposed and showed that the discussed structure is a lattice. Thus we have both a way of generating continuous t-norms from continuous t-norms and also obtain an order on them.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

FUZZY SET SYST

ISSN

0165-0114

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

1-16

Kód UT WoS článku

000997573800001

EID výsledku v databázi Scopus

2-s2.0-85138517901