Topology on residuated lattices for biresiduum-based continuity of fuzzy sets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73633483" target="_blank" >RIV/61989592:15310/25:73633483 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0165011424002793" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011424002793</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2024.109133" target="_blank" >10.1016/j.fss.2024.109133</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Topology on residuated lattices for biresiduum-based continuity of fuzzy sets

Popis výsledku v původním jazyce

By continuity of [0,1]-valued fuzzy set it is usually understood standard continuity of a real-valued function. This could be in conflict with the similarity fuzzy relation on [0,1] given by the operation of biresiduum induced by a left-continuous t-norm. In this work, a new kind of continuity, called t-continuity, of an L-set in a topological space for L being a complete residuated lattice of finite dimension is defined. It is based on a notion of oscillation of L-set, which is an element of L computed by means of biresiduum in L. A topology on L of this continuity, called the t-topology on L, is found. This topology is constructed by means of biresiduum and a variant of Scott-open sets called residuated Scott-open sets. It is shown that the t-topology of L is Hausdorff and that L together with its t-topology is a topological residuated lattice. T-topologies of four standard t-norms are found. The notion of t-topology is generalized to sets with L-equivalence relation and a new characteristic of extensional sets implying that extensional L-sets are t-continuous is given.

Název v anglickém jazyce

Topology on residuated lattices for biresiduum-based continuity of fuzzy sets

Popis výsledku anglicky

By continuity of [0,1]-valued fuzzy set it is usually understood standard continuity of a real-valued function. This could be in conflict with the similarity fuzzy relation on [0,1] given by the operation of biresiduum induced by a left-continuous t-norm. In this work, a new kind of continuity, called t-continuity, of an L-set in a topological space for L being a complete residuated lattice of finite dimension is defined. It is based on a notion of oscillation of L-set, which is an element of L computed by means of biresiduum in L. A topology on L of this continuity, called the t-topology on L, is found. This topology is constructed by means of biresiduum and a variant of Scott-open sets called residuated Scott-open sets. It is shown that the t-topology of L is Hausdorff and that L together with its t-topology is a topological residuated lattice. T-topologies of four standard t-norms are found. The notion of t-topology is generalized to sets with L-equivalence relation and a new characteristic of extensional sets implying that extensional L-sets are t-continuous is given.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

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

1872-6801

Svazek periodika

498

Číslo periodika v rámci svazku

JAN

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

13

Strana od-do

"109133-1"-"109133-13"

Kód UT WoS článku

001322230700001

EID výsledku v databázi Scopus

2-s2.0-85204459237