Isotone Galois Connections and Generalized One-Sided Concept Lattices

  • Peter ButkaEmail author
  • Jozef Pócs
  • Jana Pócsová
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 833)


We provide an approach to one-sided (crisp-fuzzy) concept lattices based on isotone Galois connections. Isotone Galois connections and concept lattices provide an alternative to the classical, antitone Galois connections based concept lattices, which are fundamental structures in formal concept analysis of object-attribute models with many-valued attributes. Our approach is suitable for analysis of data tables with different structures for truth values of particular attributes. A possible applications of this approach for approximation of object subsets is also presented.


Isotone Galois connection One-sided concept lattice Closure operator Interior operator Formal concept analysis 



The first author was supported the Slovak VEGA grant no. 1/0493/16 and Slovak APVV grant no. APVV-16-0213. The second author was supported by the project of Grant Agency of the Czech Republic (GAČR) no. 18-06915S and by the Slovak Research and Development Agency under the contract no. APVV-16-0073. The third author was supported by the Slovak Research and Development Agency under the contract no. APVV-14-0892.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Cybernetics and Artificial Intelligence, Faculty of Electrical Engineering and InformaticsTechnical University of KošiceKošiceSlovakia
  2. 2.Department of Algebra and Geometry, Faculty of SciencePalacký University OlomoucOlomoucCzech Republic
  3. 3.Mathematical Institute, Slovak Academy of SciencesKošiceSlovakia
  4. 4.Institute of Control and Informatization of Production Processes, BERG FacultyTechnical University of KošiceKošiceSlovakia

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