Fuzzy probabilistic approximation spaces and their information measures

被引：250

作者：

Hu, QH ^{[1
]}

Yu, DR ^{[1
]}

Xie, ZX ^{[1
]}

Liu, JF ^{[1
]}

机构：

[1] Harbin Inst Technol, Harbin 150001, Heilonghiang, Peoples R China

来源：

IEEE TRANSACTIONS ON FUZZY SYSTEMS | 2006年 / 14卷 / 02期

关键词：

approximation space; fuzzy set; information measure; probability distribution; rough set;

D O I：

10.1109/TFUZZ.2005.864086

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Rough set theory has proven to be an efficient tool for modeling and reasoning with uncertainty information. By introducing probability into fuzzy approximation space, a theory about fuzzy probabilistic approximation spaces is proposed in this paper, which combines three types of uncertainty: probability, fuzziness, and roughness into a rough set model. We introduce Shannon's entropy to measure information quantity implied in a Pawlak's approximation space, and then present a novel representation of Shannon's entropy with a relation matrix. Based on the modified formulas, some generalizations of the entropy are proposed to calculate the information in a fuzzy approximation space and a fuzzy probabilistic approximation space, respectively. As a result, uniform representations of approximation spaces and their information measures are formed with this work.

引用

页码：191 / 201

页数：11

共 44 条

[1]

[Anonymous], 2002, CHINESE J COMPUTERS

[2] Uncertainty measure on fuzzy partitions [J].

Bertoluzza, C ;

Doldi, V ;

Naval, G .

FUZZY SETS AND SYSTEMS, 2004, 142 (01) :105-116

[3] An axiomatic approach to fuzzy cardinalities of finite fuzzy sets [J].

Casasnovas, J ;

Torrens, J .

FUZZY SETS AND SYSTEMS, 2003, 133 (02) :193-209

[4]

DEFERIET JK, 1967, INFORM PROBABILITI A, V265, P110

[5] ROUGH FUZZY-SETS AND FUZZY ROUGH SETS [J].

DUBOIS, D ;

PRADE, H .

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 1990, 17 (2-3) :191-209

[6]

Dubois D., 1992, Putting Rough Sets and Fuzzy Sets Together, P203, DOI [10.1007/978-94-015-7975-9_14, DOI 10.1007/978-94-015-7975-9_14]

[7]

FORTE B, 1969, RIRO, V2, P63

[8] Rough sets methodology for sorting problems in presence of multiple attributes and criteria [J].

Greco, S ;

Matarazzo, B ;

Slowinski, R .

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2002, 138 (02) :247-259

[9] A reformulation of entropy in the presence of indistinguishability operators [J].

Hernández, E ;

Recasens, J .

FUZZY SETS AND SYSTEMS, 2002, 128 (02) :185-196

[10] Learning rules from incomplete training examples by rough sets [J].

Hong, TP ;

Tseng, LH ;

Wang, SL .

EXPERT SYSTEMS WITH APPLICATIONS, 2002, 22 (04) :285-293

← 1 2 3 4 5 →