Upper Boundary Algebra for Modeling the Missing Values Is a Residuated Lattice

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F24%3AA2502NM5" target="_blank" >RIV/61988987:17610/24:A2502NM5 - isvavai.cz</a>

Výsledek na webu

<a href="https://ieeexplore.ieee.org/document/10612160" target="_blank" >https://ieeexplore.ieee.org/document/10612160</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/FUZZ-IEEE60900.2024.10612160" target="_blank" >10.1109/FUZZ-IEEE60900.2024.10612160</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Upper Boundary Algebra for Modeling the Missing Values Is a Residuated Lattice

Popis výsledku v původním jazyce

It is already more than 100 years since the first proposal on three-valued logic appeared and it became a seminal work initiating lots of followers among scholars and researchers. Since then, we have observed distinct logical and algebraic approaches to modeling undefined values. These various algebraic models of three-valued functionality are built to model various types of undefinedness, e.g., conceptional undefinedness, inconsistencies, indeterminable values, meaningless values, or half-true. It is not surprising that recently, these three-valued logics have been extended to partial fuzzy logics, i.e. specific many-valued logics that are extended by the dummy value that models the undefined truth value. The algebraic structures for such logics are called partial algebras. Recently, two partial algebras, namely the Dragonfly algebra and the Lower Estimation, were both developed to capture the missing or unknown values. Their main idea consists in determining the lower boundary of the truth value of a proposition that we may guarantee after processing the operations independently on what values would replace the dummies one. Such an approach naturally leads to the consequence that the dummy value behaves as a "nearly-zero" or "almost-false" value. Though the application potential of such algebras in processing the missing values turned out to be very useful at some problems, it turned to be promising to consider a nearly dual approach. Such an approach should model the upper boundary idea and lead to a "nearly-one" or "almost-true" value. This study provides the first definition of such an algebra and investigates which of the standard properties of residuated lattices remain preserved. Unlike in the lower boundary case, we surprisingly show that in principle all of them are preserved, i.e., that the Upper Boundary algebra, though extended, remains to be the residuated lattice.

Název v anglickém jazyce

Upper Boundary Algebra for Modeling the Missing Values Is a Residuated Lattice

Popis výsledku anglicky

It is already more than 100 years since the first proposal on three-valued logic appeared and it became a seminal work initiating lots of followers among scholars and researchers. Since then, we have observed distinct logical and algebraic approaches to modeling undefined values. These various algebraic models of three-valued functionality are built to model various types of undefinedness, e.g., conceptional undefinedness, inconsistencies, indeterminable values, meaningless values, or half-true. It is not surprising that recently, these three-valued logics have been extended to partial fuzzy logics, i.e. specific many-valued logics that are extended by the dummy value that models the undefined truth value. The algebraic structures for such logics are called partial algebras. Recently, two partial algebras, namely the Dragonfly algebra and the Lower Estimation, were both developed to capture the missing or unknown values. Their main idea consists in determining the lower boundary of the truth value of a proposition that we may guarantee after processing the operations independently on what values would replace the dummies one. Such an approach naturally leads to the consequence that the dummy value behaves as a "nearly-zero" or "almost-false" value. Though the application potential of such algebras in processing the missing values turned out to be very useful at some problems, it turned to be promising to consider a nearly dual approach. Such an approach should model the upper boundary idea and lead to a "nearly-one" or "almost-true" value. This study provides the first definition of such an algebra and investigates which of the standard properties of residuated lattices remain preserved. Unlike in the lower boundary case, we surprisingly show that in principle all of them are preserved, i.e., that the Upper Boundary algebra, though extended, remains to be the residuated lattice.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/EH22_008%2F0004583" target="_blank" >EH22_008/0004583: Excelentní výzkum v oblasti digitálních technologií a wellbeingu</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název statě ve sborníku

2024 Internaional Conference on Fuzzy Systems (FUZZ)

ISBN

979-8-3503-1954-5

ISSN

1558-4739

e-ISSN

1544-5615

Počet stran výsledku

7

Strana od-do

1-7

Název nakladatele

IEEE

Místo vydání

—

Místo konání akce

Yokohama

Datum konání akce

30. 6. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001293753100102