Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

Roberto G. Aragón, Jesús Medina and Eloísa Ramírez-Poussa
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Roberto G. Aragón: Department of Mathematics, University of Cádiz, 11510 Puerto Real, Cádiz, Spain
Jesús Medina: Department of Mathematics, University of Cádiz, 11510 Puerto Real, Cádiz, Spain
Eloísa Ramírez-Poussa: Department of Mathematics, University of Cádiz, 11510 Puerto Real, Cádiz, Spain

Mathematics, 2021, vol. 9, issue 5, 1-15

Abstract: The detection of redundant or irrelevant variables (attributes) in datasets becomes essential in different frameworks, such as in Formal Concept Analysis (FCA). However, removing such variables can have some impact on the concept lattice, which is closely related to the algebraic structure of the obtained quotient set and their classes. This paper studies the algebraic structure of the induced equivalence classes and characterizes those classes that are convex sublattices of the original concept lattice. Particular attention is given to the reductions removing FCA’s unnecessary attributes. The obtained results will be useful to other complementary reduction techniques, such as the recently introduced procedure based on local congruences.

Keywords: Formal Concept Analysis; equivalence relations; attribute reduction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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