Basic theorem of fuzzy concept lattices revisited
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73588501" target="_blank" >RIV/61989592:15310/18:73588501 - isvavai.cz</a>
Výsledek na webu
<a href="https://www.sciencedirect.com/science/article/pii/S0165011417301604" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011417301604</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2017.04.007" target="_blank" >10.1016/j.fss.2017.04.007</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Basic theorem of fuzzy concept lattices revisited
Popis výsledku v původním jazyce
There are two versions of the basic theorem of L-concept lattices for L being a complete residuated lattice, both proved by Belohlavek: the crisp order version and the fuzzy order version. We introduce a third version, equivalent to the fuzzy order version, but simpler and related more closely to the classical Wille's basic theorem of concept lattices. Then we use it to prove some new results on substructures of L-concept lattices and show a simpler proof of a known result on factor structures of L-concept lattices. We show by means of several counterexamples that the crisp order version does not describe the structure of L-concept lattices sufficiently. We argue that in order to formulate and prove theoretical results on L-concept lattices that are similar to those known from classical formal concept analysis, it is essential to use the fuzzy order version of the basic theorem. We also discuss the correspondence between the Belohlavek's fuzzy order version of the basic theorem and the version introduced in this paper.
Název v anglickém jazyce
Basic theorem of fuzzy concept lattices revisited
Popis výsledku anglicky
There are two versions of the basic theorem of L-concept lattices for L being a complete residuated lattice, both proved by Belohlavek: the crisp order version and the fuzzy order version. We introduce a third version, equivalent to the fuzzy order version, but simpler and related more closely to the classical Wille's basic theorem of concept lattices. Then we use it to prove some new results on substructures of L-concept lattices and show a simpler proof of a known result on factor structures of L-concept lattices. We show by means of several counterexamples that the crisp order version does not describe the structure of L-concept lattices sufficiently. We argue that in order to formulate and prove theoretical results on L-concept lattices that are similar to those known from classical formal concept analysis, it is essential to use the fuzzy order version of the basic theorem. We also discuss the correspondence between the Belohlavek's fuzzy order version of the basic theorem and the version introduced in this paper.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Návaznosti výsledku
Projekt
<a href="/cs/project/EE2.3.20.0059" target="_blank" >EE2.3.20.0059: Reintegrace českého vědce a vytvoření špičkového týmu v informačních vědách</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2018
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
FUZZY SETS AND SYSTEMS
ISSN
0165-0114
e-ISSN
—
Svazek periodika
333
Číslo periodika v rámci svazku
FEB
Stát vydavatele periodika
NL - Nizozemsko
Počet stran výsledku
17
Strana od-do
54-70
Kód UT WoS článku
000418598800006
EID výsledku v databázi Scopus
2-s2.0-85018674286