粗糙集理论中核概念的讨论

Discussion on core concept of rough set

核是粗糙集理论的基本概念之一,为使获取的知识规则更简洁、更易于理解,许多算法都以先求出信息系统的核为基础进行启发式搜索以求取信息系统属性集的最小约简.通过实例验证,发现了许多文献中核的定义与核的计算之间存在矛盾冲突,这一矛盾冲突导致众多属性约简算法普遍存在核基为0时无法有效地进行属性约简的缺陷.针对核概念的这一问题及由此引起的属性约简算法的缺陷,对粗糙集理论中核的概念进行了重新定义,将核的定义统一于核的计算,提出了真核和伪核两个新概念,并给出了这两个新概念的相关定理及证明.

Core is one of basic concepts of rough set theory. For getting knowledge regulations being more concise and more understandable, based on a information system＇s core many algorithms firstly carry a minimal reduction of the information system ＇s attribute set through heuristic searching. By validating a practical instance, this paper finds a conflict between the definiting of core and the computing of core in many literatures and the conflict leads to a flaw which widely exists in many attribute reduction algorithms when the cardinal number of core equals zero. Aim at the conflict and flaw this paper redefines the core concept of rough set, replaces the definition of core with computing of core, presents two new concepts, called hypo-core and real-core, and a series of their concerning theorems being proved.