形式概念分析中的同效关系与概念约简

Same Effect Relation and Concept Reduction in Formal Concept Analysis

2018年以来,学者们在形式概念分析中提出并研究了“概念约简”的新课题,包括不必要概念、核心概念、相对必要概念这3类概念的鉴别研究,以及概念约简算法的研究。文中提出了同效关系,研究了其重要性质,给出了通过同效关系鉴别3类概念的简单的方法,并给出了由同效关系子集补集的概念格来得到概念约简的新算法。多年来,“约简课题”的算法都是使用合取范式和析取范式相互转换的方法,很多学者甚至表示“约简问题”就等同于合取范式和析取范式的转换问题。文中研究了不使用合取范式和析取范式转换来解决“约简课题”的新方法。该新方法不论是在理论上还是在实践上都极具意义,是一次新的尝试。一个背景的“概念约简”往往非常多,全部求出没有太大意义,一般需要求包含某些概念的“概念约简”,而所提方法在这方面具有显著的优越性。

Since 2018,scholars have proposed and studied a new topic of“concept reduction”in formal concept analysis.Including unnecessary concepts,core concepts,relatively necessary concepts,and the identification of three types of concepts,and research on concept reduction algorithm.In this paper,the same effect relation is proposed and its important properties are studied.It pre-sents a simple way to identify three types of concepts through the same effect relationship,and proposes a new algorithm for concept reduction which is based on the concept lattice of the complement set of subsets of the same effect relationship.For decades,the algorithm of“reduction topic”has adopted the method of conjunctive normal form and disjunctive normal form transformation.Many scholars even said that“reduction problem”was equivalent to the transformation of conjunctive paradigm and disjunctive paradigm.This paper studies a new method to solve the“reduction problem”without using the transformation between conjunctive normal form and disjunctive normal form.This new method is of significance both in theory and in practice.It is a new attempt.There are often many“concept reduction”in a background,so it is not very meaningful to find out all the results.Gene-rally,it is necessary to find out“concept reduction”containing some concepts,and the method in this paper has particular advantages in this respect.