Probabilistic formal concepts with negation

E. E. Vityaev, V. V. Martinovich

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

8 Citations (Scopus)


The probabilistic generalization of formal concept analysis, as well as it’s comparison to standard formal analysis is presented. Construction is resistant to noise in the data and give one an opportunity to consider contexts with negation (object-attribute relation which allows both attribute presence and it’s absence). This generalization is obtained from the notion of formal concepts with its definition as fixed points of implications, when implications, possibly with negations, are replaced by probabilistic laws. We prove such fixed points (based on the probabilistic implications) to be consistent and wherefore determine correct probabilistic formal concepts. In the end, the demonstration for the probabilistic formal concepts formation is given together with noise resistance example.

Original languageEnglish
Title of host publicationPerspectives of System Informatics - 9th International Ershov Informatics Conference, PSI 2014, Revised Selected Papers
EditorsIrina Virbitskaite, Andrei Voronkov, Irina Virbitskaite
PublisherSpringer-Verlag GmbH and Co. KG
Number of pages15
ISBN (Print)9783662468227
Publication statusPublished - 2015
Event9th International Ershov Informatics Conference on Perspectives of System Informatics, PSI 2014 - St. Petersburg, Russian Federation
Duration: 24 Jun 201427 Jun 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International Ershov Informatics Conference on Perspectives of System Informatics, PSI 2014
CountryRussian Federation
CitySt. Petersburg


  • Association rules
  • Data mining
  • Formal concept analysis
  • Noise
  • Probability


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