Approximating Fuzzy Relation Equations Through Concept Lattices.

Fuzzy relation equations (FRE) is a formal theory broadly studied in the literature and applied to decision making, optimization problems, image processing, etc. It is usual that the initial data contains uncertain, imperfect or incomplete information, which can imply, for instance, the existence of inconsistencies. As a consequence, the FRE that arises from the data may be unsolvable. Taking advantage of the relationship between FRE and concept lattices, this paper is focused on three mechanisms for approximating unsolvable FRE. Several properties have been introduced and different distances for determining the best approximation are considered and applied to an example.