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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Preservation of properties of residuated algebraic structure by structures for the partial fuzzy set theory
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-07851S" target="_blank" >GA20-07851S: Fuzzy relational structures in approximate reasoning</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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