摘要:
三元概念分析是一种数据分析和信息处理的新方法.三元概念的构造是三元概念分析的重要问题之一.首先,研究一个三元概念的外延、内涵和方式中存在空集时该三元概念具有的性质,并给出这类三元概念的判定方法.其次,定义一类特殊的三元概念,称其为对象-条件三元概念.在对象-条件三元概念构成的集合上定义一种运算,并利用该运算提出一种基于对象-条件三元概念生成三元概念的方法.该方法表明：如果一个三元概念的外延和方式均为非空集合,那么它可以由某些对象-条件三元概念生成.此外,将一个三元背景按照每一个条件分解为一系列二元背景,研究该三元背景上的对象-条件三元概念与分解后的二元背景上的对象二元概念之间的关系，并进一步给出了由对象-条件三元概念生成三元概念的具体步骤.最后,通过实例阐明由对象-条件三元概念构造三元概念的详细过程,并给出了三元图来清晰地描述所生成的所有三元概念.
Abstract:
Triadic concept analysis is a new approach for data analysis and information processing. One of the important problems of triadic concept analysis is the construction of triadic concepts. Firstly, properties of a triadic concept in which one of its extent, intent and modus is an empty set are studied, and the judgment method of this kind of triadic concept is also obtained. Secondly, another kind of special triadic concept, called object-conditional triadic concept, is researched in detail. An operation is defined on the set of conditional triadic concepts, and a construction method of triadic concepts is then proposed based on object-conditional triadic concepts using the operation. It is shown that every triadic concept can be generated by some object-conditional triadic concepts if its extent and modus are both non-empty sets. Thirdly, a triadic context is decomposed into a series of dyadic contexts according to its conditions. The relationship between object-conditional triadic concepts of the triadic context and object dyadic concepts of those decomposed dyadic contexts is then studied. Furthermore, steps are given to generate all triadic concepts from object-conditional triadic concepts. Finally, the detailed process of constructing the triadic concepts is demonstrated by an example, and the triadic diagram is given to describe all generated triadic concepts more clearly.
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