A novel approach to fuzzy rough sets based on a fuzzy covering

被引：190
作者：
Deng, Tingquan [1 ]
Chen, Yanmei
Xu, Wenli
Dai, Qionghai
机构：
[1] Harbin Engn Univ, Coll Sci, Harbin 150001, Peoples R China
[2] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
[3] Tsinghua Univ, Dept Automat, Beijing 100084, Peoples R China
来源：
INFORMATION SCIENCES | 2007年 / 177卷 / 11期
基金：
中国国家自然科学基金;
关键词：
fuzzy logic; conjunction; implication; fuzzy covering; complete lattice; adjunction; rough sets; fuzzy rough approximations; morphological operators;
D O I：
10.1016/j.ins.2006.11.013
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This paper proposes an approach to fuzzy rough sets in the framework of lattice theory. The new model for fuzzy rough sets is based on the concepts of both fuzzy covering and binary fuzzy logical operators (fuzzy conjunction and fuzzy implication). The conjunction and implication are connected by using the complete lattice-based adjunction theory. With this theory, fuzzy rough approximation operators are generalized and fundamental properties of these operators are investigated. Particularly, comparative studies of the generalized fuzzy rough sets to the classical fuzzy rough sets and Pawlak rough set are carried out. It is shown that the generalized fuzzy rough sets are an extension of the classical fuzzy rough sets as well as a fuzzification of the Pawlak rough set within the framework of complete lattices. A link between the general-ized fuzzy rough approximation operators and fundamental morphological operators is presented in a translation-invariant additive group. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：2308 / 2326
页数：19
相关论文
共 46 条
[1]  
BISWAS R, 1994, B POLISH ACAD SCI MA, V42, P351
[2]  
Biswas R., 1994, Bulletin of the Polish Academy of Sciences Mathematics, V42, P345
[3]   On links between mathematical morphology and rough sets [J].
Bloch, I .
PATTERN RECOGNITION, 2000, 33 (09) :1487-1496
[4]   Approximation of fuzzy concepts in decision making [J].
Bodjanova, S .
FUZZY SETS AND SYSTEMS, 1997, 85 (01) :23-29
[5]   Extensions and intentions in the rough set theory [J].
Bonikowski, Z ;
Bryniarski, E ;
Wybraniec-Skardowska, U .
INFORMATION SCIENCES, 1998, 107 (1-4) :149-167
[6]   Inclusion grade and fuzzy implication operators [J].
Burillo, P ;
Frago, N ;
Fuentes, R .
FUZZY SETS AND SYSTEMS, 2000, 114 (03) :417-429
[7]  
CHEN Y, 2002, CHINESE Q J MATH, V17, P70
[8]   J-partitions [J].
De Baets, B ;
Mesiar, R .
FUZZY SETS AND SYSTEMS, 1998, 97 (02) :211-223
[9]   A new approach to mining fuzzy databases using nearest neighbor classification by exploiting attribute hierarchies [J].
De, SK ;
Krishna, PR .
INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 2004, 19 (12) :1277-1290
[10]   Rough approximations on a complete completely distributive lattice with applications to generalized rough sets [J].
Degang, Chen ;
Wenxiu, Zhang ;
Yeung, Daniel ;
Tsang, E. C. C. .
INFORMATION SCIENCES, 2006, 176 (13) :1829-1848
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