Formal Equivalence Analysis
Abstract
Following R. Wille’s lead and suggestion we set out to design a new kind of view onto a formal context analogous but different to Formal Concept Analysis and Formal Independent Analysis.In this instance, we choose to analyse the information in the incidence table in terms of the partitions induced on the sets of objects and attributes by the same functions of single attributes and objects of the context.These functions constitute a left adjunction between sets of objects and attributes and we later lift this left adjunction to partitions of the objects and attributes.Therefore we refer to this new view onto the formal context as Formal Equivalence Analysis.Rather than looking on the effect of these partitions on set representation, as in Rough Sets, we try to make explicit the information in the context.
Citation
Please, cite this work as:
[Alb+19] F. J. V. Albacete, C. Peláez-Moreno, P. Cordero, et al. “Formal Equivalence Analysis”. In: Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2019, Prague, Czech Republic, September 9-13, 2019. Ed. by V. Novák, Vladim'', M. Stepnicka, M. Navara and P. Hurt'. Vol. 1. Atlantis Studies in Uncertainty Modelling. Atlantis Press, 2019. DOI: 10.2991/EUSFLAT-19.2019.109. URL: https://doi.org/10.2991/eusflat-19.2019.109.
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Papers citing this work
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[1] D. López-Rodríguez, E. Muñoz-Velasco, and M. Ojeda-Aciego. “Formal Methods in FCA and Big Data”. In: Complex Data Analytics with Formal Concept Analysis. Springer International Publishing, Dec. 2021, p. 201–224. ISBN: 9783030932787. DOI: 10.1007/978-3-030-93278-7_9. URL: http://dx.doi.org/10.1007/978-3-030-93278-7_9.
[2] F. J. Valverde-Albacete, C. Peláez-Moreno, I. P. Cabrera, et al. “Encoding Non-global Time Representations into the Lattice of Divisibility”. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer International Publishing, 2022, p. 118–129. ISBN: 9783031089718. DOI: 10.1007/978-3-031-08971-8_11. URL: http://dx.doi.org/10.1007/978-3-031-08971-8_11.