A mathematical model for concept granular computing systems

被引：22
|
作者：
Qiu GuoFang [1 ]
Ma JianMin [2 ]
Yang HongZhi [3 ]
Zhang WenXiu [3 ]
机构：
[1] Xian Univ Architecture & Technol, Sch Management, Xian 710055, Peoples R China
[2] Changan Univ, Fac Sci, Xian 710064, Peoples R China
[3] Xi An Jiao Tong Univ, Fac Sci, Xian 710049, Peoples R China
来源：
SCIENCE CHINA-INFORMATION SCIENCES | 2010年 / 53卷 / 07期
基金：
中国国家自然科学基金;
关键词：
granular computing; formal concept analysis; concept lattice; mathematical model; CONCEPT LATTICES; INFORMATION GRANULATION;
D O I：
10.1007/s11432-010-3092-z
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Extent-intent and intent-extent operators are introduced between two complete lattices in this paper and a mathematical model for concept granular computing system is established. We proved that the set of all concepts in this system is a lattice with the greatest element and the least element. This framework includes formal concept lattices from formal contexts, L fuzzy concept lattices from L fuzzy formal contexts and three kinds of variable threshold concept lattices, i.e. the extension and the intension of a concept are a crisp set and a crisp set, a crisp set and a fuzzy set, a fuzzy set and a crisp set, respectively. Finally, some iterative algorithms for constructing concepts are proposed and they are proved to be optimal concepts under some conditions in this system.
引用
收藏
页码：1397 / 1408
页数：12
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