Dualities in the class of extended Boolean functions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F18%3AA1901RRS" target="_blank" >RIV/61988987:17610/18:A1901RRS - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.fss.2017.04.008" target="_blank" >http://dx.doi.org/10.1016/j.fss.2017.04.008</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2017.04.008" target="_blank" >10.1016/j.fss.2017.04.008</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Dualities in the class of extended Boolean functions

Popis výsledku v původním jazyce

We introduce and discuss duality operators on the set of binary extended Boolean functions, i.e., on the set of binary operations on the real interval [0, 1] whose restrictions to Boolean inputs yield Boolean functions. These dualities have been divided into seven classes, and the majority of their properties depend on the class they belong to. We study composition of dualities, properties of dual classes, duality of properties of extended Boolean functions and invariantness of extended Boolean functions with respect to particular dualities. Our approach allows to transfer the results known for some studied class of extended Boolean functions into the results for the corresponding dual classes. As typical examples, one can recall the standard duality of the classes of all t-norms and t-conorms and the duality of implication functions and conjunctive (disjunctive) aggregation functions.

Název v anglickém jazyce

Dualities in the class of extended Boolean functions

Popis výsledku anglicky

We introduce and discuss duality operators on the set of binary extended Boolean functions, i.e., on the set of binary operations on the real interval [0, 1] whose restrictions to Boolean inputs yield Boolean functions. These dualities have been divided into seven classes, and the majority of their properties depend on the class they belong to. We study composition of dualities, properties of dual classes, duality of properties of extended Boolean functions and invariantness of extended Boolean functions with respect to particular dualities. Our approach allows to transfer the results known for some studied class of extended Boolean functions into the results for the corresponding dual classes. As typical examples, one can recall the standard duality of the classes of all t-norms and t-conorms and the duality of implication functions and conjunctive (disjunctive) aggregation functions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

FUZZY SET SYST

ISSN

0165-0114

e-ISSN

—

Svazek periodika

332

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

15

Strana od-do

78-92

Kód UT WoS článku

000417104900008

EID výsledku v databázi Scopus

2-s2.0-85018966572