概念格上的近似概念

The approximation concept of concept lattices

探讨在形式背景中的任意概念,由其外延形成的上近似概念和下近似概念,以及由其内涵形成的上近似概念和下近似概念这四者之间的关系.在形式背景中,从任意对象集(或属性集)出发,利用确定的概念格建立该对象(或属性)的下近似概念外延(或内涵)与上近似外延(或内涵),从而得到由对象(或属性)集形成的上近似概念和下近似概念;对于任意一概念,由其外延形成的上近似概念和下近似概念是它本身,且由其内涵形成的上近似概念和下近似概念也是它本身.通过实例说明这种方法的可行性,由此得到概念格理论中,生成上(下)近似概念的一种有效方法.

The notion of the formal concept in a formal context is studied in this paper.The relationship among the upper and lower approximation concepts formed respectively by the extent and intent is investigated.For any object（or attribute）set in a formal context,the lower and upper approximation concept extents（or intents）can be established via the concept lattice.Thus the lower and upper approximation concepts formed by its extent（or attribute）set can be obtained.For any concept of the concept lattice,the upper and the lower approximation concepts formed respectively by the extent and intent are all itself.Finally,an example is given to show the validity of our method for generating the upper（or lower） approximation concept of the concept lattice.