用概念格方法精简模糊关系方程，保留信息的同时减少冗余。
Reducing fuzzy relation equations via concept lattices
- 基于属性概念格的约简理论，识别并去除冗余方程。
- 求解可解的模糊关系方程时，计算量显著降低。
- 适用于含不确定数据的现实数据集，可求近似解。
本文利用模糊关系方程（FRE）与概念格之间的关联，提出一种在不丢失信息的前提下精简FRE的算法。具体而言，结合属性导向与对象导向概念格中的属性约简理论，建立检测冗余方程的机制。该方法首先降低了可解FRE全解集的计算复杂度；此外，还提出一种新方法，用于处理包含不确定性/不精确数据的实际数据集上的不可解FRE，并计算其近似解。
原文摘要 · Abstract (English)
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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