Determination of the continuous completions of conditionally cancellative pre-t-norms associated with the characterization of (S,N)-implications: Part I

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2402LNQ" target="_blank" >RIV/61988987:17610/23:A2402LNQ - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0165011423002592" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011423002592</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2023.108614" target="_blank" >10.1016/j.fss.2023.108614</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Determination of the continuous completions of conditionally cancellative pre-t-norms associated with the characterization of (S,N)-implications: Part I

Popis výsledku v původním jazyce

The continuous completions of conditionally cancellative pre-t-norms defined in the regions linked to the characterization of (S,N)-implications when Sis a continuous t-conorm and Nis a fuzzy negation with one point of discontinuity are determined. The results have been divided in two parts. In this first part we provide three main results: we determine the existence and expression of the additive generator of a cancellative pre-t-norm known above a level curve and, using this result as a basis, we provide the continuous completions of pre-t-norms determined in regions of the type [0,1]^2(0,a)^2 or [0,1]^2(a,1)^2with a ∈ (0,1). It is highlighted that, differently from the cancellative case where all the results provide unique continuous completions, in the analogous situations in the conditionally cancellative case the corresponding continuous completions might not be unique. This fact causes more complex results for the remaining regions, which are discussed in the second paper of this study.

Název v anglickém jazyce

Determination of the continuous completions of conditionally cancellative pre-t-norms associated with the characterization of (S,N)-implications: Part I

Popis výsledku anglicky

The continuous completions of conditionally cancellative pre-t-norms defined in the regions linked to the characterization of (S,N)-implications when Sis a continuous t-conorm and Nis a fuzzy negation with one point of discontinuity are determined. The results have been divided in two parts. In this first part we provide three main results: we determine the existence and expression of the additive generator of a cancellative pre-t-norm known above a level curve and, using this result as a basis, we provide the continuous completions of pre-t-norms determined in regions of the type [0,1]^2(0,a)^2 or [0,1]^2(a,1)^2with a ∈ (0,1). It is highlighted that, differently from the cancellative case where all the results provide unique continuous completions, in the analogous situations in the conditionally cancellative case the corresponding continuous completions might not be unique. This fact causes more complex results for the remaining regions, which are discussed in the second paper of this study.

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 Sets and Systems

ISSN

0165-0114

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

30

Strana od-do

—

Kód UT WoS článku

001028270300001

EID výsledku v databázi Scopus

2-s2.0-85162021815