Reducing fuzzy relation equations via concept lattices

• URL: http://arxiv.org/abs/2410.05728v1
• Date: Tue, 8 Oct 2024 06:47:35 GMT
• Title: Reducing fuzzy relation equations via concept lattices
• Authors: David Lobo, Víctor López-Marchante, Jesús Medina,
• Abstract summary: This paper introduces a procedure to reduce a Fuzzy Relation Equations (FRE) without losing information. attribute reduction theory in property-oriented and object-oriented concept lattices has been considered in order to present a mechanism for detecting redundant equations. We will also introduce a novel method for computing approximate solutions of unsolvable FRE related to a (real) dataset with uncertainty/imprecision data.
• Score: 0.5735035463793009
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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