Aggregation on lattices isomorphic to the lattice of closed subintervals of the real unit interval

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73616931" target="_blank" >RIV/61989592:15310/22:73616931 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S016501142200063X" target="_blank" >https://www.sciencedirect.com/science/article/pii/S016501142200063X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2022.02.013" target="_blank" >10.1016/j.fss.2022.02.013</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Aggregation on lattices isomorphic to the lattice of closed subintervals of the real unit interval

Popis výsledku v původním jazyce

In numerous generalizations of the original theory of fuzzy sets proposed by Zadeh, the considered membership degrees are often taken from lattices isomorphic to the lattice LI of closed subintervals of the unit interval [0, 1]. This is, for example, the case of intuitionistic values, Pythagorean values or q-rung orthopair values. The mentioned isomorphisms allow to transfer the results obtained for the lattice LI directly to the other mentioned lattices. In particular, basic connectives in Zadeh&apos;s fuzzy set theory, i.e., special functions on the lattice [0, 1], can be extended to the interval-valued connectives, i.e., to special functions on the lattice LI , and then to the connectives on the lattices L* of intuitionistic values, P of Pythagorean values, and also on the lattice L tau q of q-rung orthopair values. We give several examples of such connectives, in particular, of those which are related to strict t-norms. For all these connectives we show their link to an additive generator f of the considered strict t-norm T. Based on our approach, many results discussed in numerous papers can be treated in a unique framework, and the same is valid for possible newly proposed types of connectives based on strict t-norms. Due to this approach, a lot of tedious proofs of the properties of the proposed connectives could be avoided, which gives researchers more space for presented applications.

Název v anglickém jazyce

Aggregation on lattices isomorphic to the lattice of closed subintervals of the real unit interval

Popis výsledku anglicky

In numerous generalizations of the original theory of fuzzy sets proposed by Zadeh, the considered membership degrees are often taken from lattices isomorphic to the lattice LI of closed subintervals of the unit interval [0, 1]. This is, for example, the case of intuitionistic values, Pythagorean values or q-rung orthopair values. The mentioned isomorphisms allow to transfer the results obtained for the lattice LI directly to the other mentioned lattices. In particular, basic connectives in Zadeh&apos;s fuzzy set theory, i.e., special functions on the lattice [0, 1], can be extended to the interval-valued connectives, i.e., to special functions on the lattice LI , and then to the connectives on the lattices L* of intuitionistic values, P of Pythagorean values, and also on the lattice L tau q of q-rung orthopair values. We give several examples of such connectives, in particular, of those which are related to strict t-norms. For all these connectives we show their link to an additive generator f of the considered strict t-norm T. Based on our approach, many results discussed in numerous papers can be treated in a unique framework, and the same is valid for possible newly proposed types of connectives based on strict t-norms. Due to this approach, a lot of tedious proofs of the properties of the proposed connectives could be avoided, which gives researchers more space for presented applications.

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

2022

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

441

Číslo periodika v rámci svazku

AUG

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

17

Strana od-do

262-278

Kód UT WoS článku

000812960300012

EID výsledku v databázi Scopus

2-s2.0-85125501716