三元概念与形式概念的关系

南京大学学报(自然科学版) ›› 2018, Vol. 54 ›› Issue (4): 786–.

三元概念与形式概念的关系

李俊余1，2，朱荣杰1，王　霞1，2*，吴伟志1，2

出版日期:2018-04-30
作者简介:1.浙江海洋大学数理与信息学院，舟山，316022；2.浙江省海洋大数据挖掘与应用重点实验室，舟山，316022
基金资助:
基金项目：国家自然科学基金(61202206，61573321，41631179，61773349)，浙江省自然科学基金(LY18F030017) 收稿日期：2018－05－22 *通讯联系人，E－mail：bblylm@126.com

The relationship between triadic concepts and formal concepts

Li Junyu1，2，Zhu Rongjie1，Wang Xia1，2*，Wu Weizhi1，2

Online:2018-04-30
About author:1.School of Mathematics，Physics and Information Science，Zhejiang Ocean University，Zhoushan，316022，China； 2．Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province，Zhoushan，316022，China

摘要/Abstract

摘要： 由于三元概念分析是形式概念分析的拓展，因此三元概念和形式概念(二元概念)之间有着紧密的联系. 首先，从二元背景出发来描述三元概念，研究一个三元背景的三元概念和所有非空条件子集确定的二元背景的二元概念之间的关系. 在每一个条件确定的二元背景的所有二元对象概念集上定义一种运算，证明了通过该运算和二元概念间的并运算可以生成所有非空条件子集确定的二元背景的所有二元概念. 其次，定义了一个从二元概念到三元概念的双射，并从概念粒的角度将一个三元背景的所有三元概念和二元概念进行分层，共分为三层，其中第一层是由单个对象和条件确定的二元对象概念，由它们可以生成第二层和第三层的概念粒，因此第一层是最基本的概念粒，这对三元概念的理解和构造具有重要的作用. 最后，从三元概念出发来寻找二元概念，基于三元概念提出生成由每个条件确定的二元背景的二元概念的方法，并给出了严格证明. 此外，还通过三元图对该方法加以直观解释．

Abstract: There is a close relationship between triadic concepts and formal concepts(dyadic concepts)，since triadic concept analysis can be seen as an extension of formal concept analysis. Firstly，starting from dyadic contexts to describe triadic concepts，the relationship between all triadic concepts of a triadic context and the dyadic concepts of each dyadic context determined by each nonempty conditional subset is studied. An operation is then defined on all dyadic object concepts of the dyadic context determined by each condition. It is proved that all dyadic concepts can be generated by some dyadic object concepts using the operation and the union operation defined on the dyadic concepts. Secondly，a map from dyadic concepts to triadic concepts is defined and it is proved that the map is a bijection. Moreover，the triadic concepts and the dyadic concepts of the triadic context are stratified from the perspective of concept particles，which play an important role in understanding and constructing the triadic concepts. The first layer is composed of dyadic object concepts determined by single object and condition，and they can generate the second and third layers of concept granules，so that the first layer is the most basic concept granule. Finally，a method of generating the dyadic concepts of each dyadic context determined by each condition is presented from the triadic concepts，and proved strictly. In order to describe the method more intuitively，the triadic diagram of all triadic concepts of a triadic context is given.

李俊余1，2，朱荣杰1，王　霞1，2*，吴伟志1，2. 三元概念与形式概念的关系[J]. 南京大学学报(自然科学版), 2018, 54(4): 786–.

Li Junyu1，2，Zhu Rongjie1，Wang Xia1，2*，Wu Weizhi1，2. The relationship between triadic concepts and formal concepts[J]. Journal of Nanjing University(Natural Sciences), 2018, 54(4): 786–.

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