Dualities in the class of extended Boolean functions
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Dualities in the class of extended Boolean functions
Original language description
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.
Czech name
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Czech description
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Classification
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
Result continuities
Project
<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
FUZZY SET SYST
ISSN
0165-0114
e-ISSN
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Volume of the periodical
332
Issue of the periodical within the volume
1
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
15
Pages from-to
78-92
UT code for WoS article
000417104900008
EID of the result in the Scopus database
2-s2.0-85018966572