Preservation of properties of residuated algebraic structure by structures for the partial fuzzy set theory

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2402HYM" target="_blank" >RIV/61988987:17610/23:A2402HYM - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0888613X22002134" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0888613X22002134</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ijar.2022.12.001" target="_blank" >10.1016/j.ijar.2022.12.001</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Preservation of properties of residuated algebraic structure by structures for the partial fuzzy set theory

Popis výsledku v původním jazyce

This paper addresses the preservation of numerous essential properties of a residuated lattice structure in extended algebras for partial fuzzy set theory and partial fuzzy logics. The preservation includes the residuated lattice axioms, the identities narrowing the classes of the residuated lattices, and some well-known additional properties. In this paper, we consider nine algebras for partial fuzzy logics which incorporate handling undefined values in a bit different way. In particular, we consider the Bochvar, the Bochvar external, the Sobociński, the Kleene, the McCarthy, the Nelson, and the Łukasiewicz algebras, and two recently developed ones, namely the Lower estimation and the Dragonfly algebras. We summarize the obtained results in a comprehensible form which allows readers to easily check the information for the preserved and non-preserved properties in a certain partial algebraic structure. The resulting shape of the contribution is a sort of “atlas book” that aims at providing researchers with a comfortable and comprehensible form of an overview of the (non)preservation of fundamental properties of residuated structures.

Název v anglickém jazyce

Preservation of properties of residuated algebraic structure by structures for the partial fuzzy set theory

Popis výsledku anglicky

This paper addresses the preservation of numerous essential properties of a residuated lattice structure in extended algebras for partial fuzzy set theory and partial fuzzy logics. The preservation includes the residuated lattice axioms, the identities narrowing the classes of the residuated lattices, and some well-known additional properties. In this paper, we consider nine algebras for partial fuzzy logics which incorporate handling undefined values in a bit different way. In particular, we consider the Bochvar, the Bochvar external, the Sobociński, the Kleene, the McCarthy, the Nelson, and the Łukasiewicz algebras, and two recently developed ones, namely the Lower estimation and the Dragonfly algebras. We summarize the obtained results in a comprehensible form which allows readers to easily check the information for the preserved and non-preserved properties in a certain partial algebraic structure. The resulting shape of the contribution is a sort of “atlas book” that aims at providing researchers with a comfortable and comprehensible form of an overview of the (non)preservation of fundamental properties of residuated structures.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA20-07851S" target="_blank" >GA20-07851S: Fuzzy relační struktury v přibližném usuzování</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

INT J APPROX REASON

ISSN

0888-613X

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

March

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

26

Strana od-do

1-26

Kód UT WoS článku

000916282000001

EID výsledku v databázi Scopus

2-s2.0-85144819692