On a new classification of triangular norms

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2502I2X" target="_blank" >RIV/61988987:17610/23:A2502I2X - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0165011422003748" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011422003748</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2022.09.002" target="_blank" >10.1016/j.fss.2022.09.002</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On a new classification of triangular norms

Popis výsledku v původním jazyce

In this paper, we introduce the notion of (k)-triangular norms and present a new classification of triangular norms (t-norms for short) splitting the set T of all t-norms into an infinite countable partition {T1⁎,T2⁎,…}∪{T⁎}. From the four basic t-norms, the minimum TM is the unique member of T1⁎, the drastic product TD belongs to T2⁎, the product TP and also the Łukasiewicz t-norm TL are members of T⁎. We show that t-norms from Tk⁎ are always (k+1)-contractive, but not vice-versa. We also provide some necessary and some sufficient conditions for t-norms to be (proper) (k)-t-norms. In the end, we give several examples and construction methods for t-norms belonging to particular classes of the proposed partition or to the set Tk=⋃i=1kTi⁎.

Název v anglickém jazyce

On a new classification of triangular norms

Popis výsledku anglicky

In this paper, we introduce the notion of (k)-triangular norms and present a new classification of triangular norms (t-norms for short) splitting the set T of all t-norms into an infinite countable partition {T1⁎,T2⁎,…}∪{T⁎}. From the four basic t-norms, the minimum TM is the unique member of T1⁎, the drastic product TD belongs to T2⁎, the product TP and also the Łukasiewicz t-norm TL are members of T⁎. We show that t-norms from Tk⁎ are always (k+1)-contractive, but not vice-versa. We also provide some necessary and some sufficient conditions for t-norms to be (proper) (k)-t-norms. In the end, we give several examples and construction methods for t-norms belonging to particular classes of the proposed partition or to the set Tk=⋃i=1kTi⁎.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10100 - 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 Sets and Systems

ISSN

0165-0114

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

30 August 2023

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

11

Strana od-do

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Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85137894912