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arXiv · 2410.05728

Reducing fuzzy relation equations via concept lattices

David Lobo·Víctor López-Marchante·Jesús Medina
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Abstract

This paper has taken into advantage the relationship between Fuzzy Relation Equations (FRE) and Concept Lattices in order to introduce a procedure to reduce a FRE, without losing information. Specifically, attribute reduction theory in property-oriented and object-oriented concept lattices has been considered in order to present a mechanism for detecting redundant equations. As a first consequence, the computation of the whole solution set of a solvable FRE is reduced. Moreover, we will also introduce a novel method for computing approximate solutions of unsolvable FRE related to a (real) dataset with uncertainty/imprecision data.

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David Lobo, Víctor López-Marchante, Jesús Medina. 2024-10-08. Reducing fuzzy relation equations via concept lattices. https://doi.org/10.1016/j.fss.2022.12.021

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