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Basic theorem of fuzzy concept lattices revisited

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Basic theorem of fuzzy concept lattices revisited

  • Original language description

    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&apos;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&apos;s fuzzy order version of the basic theorem and the version introduced in this paper.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

    <a href="/en/project/EE2.3.20.0059" target="_blank" >EE2.3.20.0059: Reintegration of Czech Scientist and Creation of Top Level Team in Information Sciences</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 SETS AND SYSTEMS

  • ISSN

    0165-0114

  • e-ISSN

  • Volume of the periodical

    333

  • Issue of the periodical within the volume

    FEB

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    17

  • Pages from-to

    54-70

  • UT code for WoS article

    000418598800006

  • EID of the result in the Scopus database

    2-s2.0-85018674286