摘要
粒计算是在Zadeh教授提出的模糊信息粒化思想的基础上,逐渐发展起来的一个有效处理信息的数学工具.粒计算利用粒化信息的思想解决复杂问题,而在信息粒化的过程中通常都伴随着粒描述.所谓粒描述,是指在没有明确粒化准则的情况下如何描述目标概念或论域子集.因此,粒描述是采用粒计算思维解决复杂问题的前提和基础,进一步研究将有利于粒的理解与解释.众所周知,现有的粒描述主要集中在共性属性分析的基础上开展相关研究,其核心的理论工具是形式概念分析与粗糙集.共性属性分析刻画了粒的共性,即粒中每个对象均拥有的属性.然而,现实中一个粒具有的属性有时不单指粒中所有对象共同拥有的属性,还有可能指粒中部分对象共同拥有的属性,甚至有时只需要粒中存在一个对象拥有该属性即可.实际上,共性属性分析强调的是所有对象共同拥有的属性才是这个粒的属性.与共性属性分析不同,必然属性分析强调的是只属于这个粒的属性才是它的属性.换言之,必然属性分析讨论粒描述时,除了涉及所有对象共同拥有的属性,还可能涉及部分对象共同拥有的属性.目前,从必然属性分析的角度研究粒描述尚未被详细讨论.该文基于形式概念分析中粒的思想和粗糙集理论中上、下近似的方法对这一问题展开研究.首先,介绍了必然属性分析视角下的粒描述逻辑.其次,分别基于形式背景及其补背景研究了粒描述.具体地,利用形式背景描述粒具有的必然属性,利用补背景描述粒不具有的必然属性.此外,定义了一元描述子用来特指形式背景及其补背景的面向对象概念格中的概念内涵,进而通过一个一元描述子刻画一个一元可定义粒,将一对一元描述子作为上、下近似以刻画一个一元不可定义粒.然后,为了同时使用形式背景及其补背景的信息,提出了基于必然属性分析
Granular computing is an effective mathematical tool of dealing with information and can be considered as an extension of the idea of fuzzy information granularity proposed by professor Zadeh. To the best of our knowledge, granular computing solves complicated problems via information granularity. It should be pointed out that information granularity is often accompanied by granule description. The so-called granule description is to describe a target concept or a subset of a universe of discourse when specific granularity principles are not available. Therefore, granule description is the foundation and basis of solving complicated problems by granular computing, and any further researches can be beneficial to the understanding and explanation of granules. As is well-known, the existing study on granule description is mainly based on common attribute analysis, and the key theoretical tools are formal concept analysis and rough set. Common attribute analysis characterizes the commonness of a granule by extracting the common attributes possessed by all the objects of the granule. However, an attribute a granule has in the real world, may not only be the one possessed by all the objects of the granule, but also be the one possessed by part of objects of the granule, or even sometimes the one possessed by an object of the granule. In fact, common attribute analysis emphasizes that the attribute a granule has must be the one possessed by all the objects of the granule. Different from common attribute analysis, necessary attribute analysis emphasizes that the attribute a granule has is the one belonging to the granule only. In other words, besides the attributes possessed by all the objects of a granule, necessary attribute analysis of granule description may also involve the attributes possessed by part of objects of the granule. Currently, it still lacks of a thorough study on granule description from the perspective of necessary attribute analysis. In this paper, this problem is investigated by incorporating the id
作者
智慧来
李金海
ZHI Hui-Lai;LI Jin-Hai(School of Computer Science and Technology,Henan Polytechnic University,Jiaozuo,Henan 454000;Data Science Research Center,Kunming University of Science and Technology,Kunming 650500;Faculty of Science,Kunming University of Science and Technology,Kunming 650500)
出处
《计算机学报》
EI
CSCD
北大核心
2018年第12期2702-2719,共18页
Chinese Journal of Computers
基金
国家自然科学基金(61502150
61562050
61305057
61573173)资助~~
关键词
粒计算
粒描述
形式概念分析
必然属性分析
粗糙集
三支概念格
granular computing
granule description
formal concept analysis
necessary attribute analysis
rough set
three - way concept lattice
