文章快速检索 高级检索

1. 新疆财经大学 计算机科学与工程学院，新疆 乌鲁木齐 830012;
2. 闽南师范大学 粒计算实验室，福建 漳州 363000

Linguistic dynamic systems based on covering-based rough sets
TANG Jianguo1, WANG Jianghua1, HAN Liying1, ZHU Feng2
1. School of Computer Science and Engineering, Xinjiang University of Finance and Economics, Urumqi 830012, China ;
2. Lab of Granular Computing, Minnan Normal University, Zhangzhou 363000, China
Abstract: Linguistic dynamic systems(LDS)make computing and reasoning by using words. In this way,LDS provides an effective measure to describe large complex systems. However, words have major uncertainties with describing things. This causes serious challenges for LDS. Covering-based rough sets have distinctly unique advantages in dealing with uncertain problems. This paper details how they can be effective with solving the problems in LDS. Firstly, the words in languages are represented by using the form of covering blocks; secondly, mappings of the state equation, output equation and feedback control are established by using the thought of the lower and upper approximations, then a LDS model based on the covering-based rough sets is obtained;thirdly, an inference method of the model is proposed to analyze and solve real problems; finally,the validity and the efficiency of the model and the inference method have been proved by some instance analysis.
Key words: rough set theory     artificial intelligence     data mining     linguistics     control theory     granular computing     approximation theory     knowledge acquisition

1 相关定义

1.1 覆盖粗糙集

U是一个论域，CU的一个子集族。如果C中的所有子集都不空，且∪C=U，则称CU的一个覆盖；称有序对(U,C)为覆盖近似空间。对于任意一个子集XU，定义X关于C的下近似和上近似分别为：

 (1)
 (2)

 (3)
 (4)

 (5)

 (6)
1.2 语言动力系统

2 问题的提出

3 覆盖粗糙集的LDS模型 3.1 模型

3.2 推理方法

1)将语言描述的背景知识转换为覆盖形式的知识。粗糙集中认为知识是一种分类能力，并将每类事物都用一个集合来表示。在覆盖粗糙集中，这些类对应的集合被称为覆盖块。于是，为了求解问题需要先将已有的知识转换为反映分类能力的覆盖。具体来说，首先要依据实际问题来获得论域U，其次再根据已有知识得到覆盖C，最后为了实现用自然语言来描述计算结果，需要给予覆盖中的每个覆盖块一个语言标签ω

①根据实际情况确定论域U

②根据对问题的已有知识来获得U上的覆盖C={K1,K2,…,Kn}；

③根据问题的具体情况给各覆盖块添加语言标签，其中，∀KiC

2)将要求解的问题转换成目标集合。通过分析问题的特点，将问题转换为目标集合X

3)根据得到的覆盖和式(3)、(4)求得目标集合X

4)根据来得出确定成立和可能成立的知识。在这一过程中，一方面要根据问题给出描述结论的2种语言范式，即描述确定成立知识和描述可能成立知识的语言范式。另一方面，需要结合1)中的ω(C)来实现计算结果的语言表示。

abcd是4个任意实数，其中abcdA=[a,b]和B=[c,d]是2个数值区间。定义AB的交运算、并运算以及子集等关系如下：

1)AB

acbd，则AB=[a,b]；

accbd，则AB=[c,b]；

acb>d，则AB=[c,d]；

b <ca>d

2)AB

acbd，则AB=[c,d]；

cab>d，则AB=[c,b]；

acbd，则AB=[a,d]；

acb>d，则AB=[a,b]。

3)AB

cabd，则称AB的子集，记为AB

4)AB

a=bAB，则称A属于B，记为AB

5)A=B

a=cb=d，则称A等于B，记为A=B

4 实例与分析

1)根据已知条件可知学生的成绩分数范围为［0,100]，即：论域U=[0,100]；

ω(C)={优,良,中,差}，其中，ω(K1)=优，ω(K2)=良，ω(K3)=中，ω(K4)=差。

2)由于小明的成绩等级为“中”，其对应的成绩为(65,80)，也就是说小明的具体成绩可以是这个区间中的任何一个实数。若令小明的成绩为a(65<a<80)，则对于任意b(80≤b≤100)，都满足b>a，也就是说成绩为b要好于成绩a。于是，将[80,100]看作目标集合X，即：X=[80,100]。

3)根据得到的CX可知，在C中只有覆盖块K=(85,100]⊆X，其余覆盖块均不是X的子集。根据式(3)可得

4)给出描述结论的2种语言范式。

①确定成立知识的语言范式。

“成绩等级为“ω(K)”的学生成绩“一定”比小明的成绩好。”这里

②可能成立知识的语言范式。

“成绩等级为“ω(K)”的学生成绩“可能”比小明的成绩好。”这里

ω(K1)=“优”可得

“成绩等级为“优”的学生成绩“一定”比小明的成绩好。”

“成绩等级为“良”的学生成绩“可能”比小明的成绩好。”

“小明的成绩等级“可能”为“ω(K)””。

“小明的成绩等级‘可能’为‘中’”。

“小明的成绩等级‘可能’为‘良’”。

5 结束语

 [1] WANG Feiyue. Modeling,analysis and synthesis of linguistic dynamic systems: a computational theory[C]//IEEE International Workshop on Architecture for Semiotic Modeling and Situation Control in Large Complex Systems. Monterey,CA,1995: 173-178. [2] 王飞跃. 词计算和语言动力学系统的计算理论框架[J]. 模式识别与人工智能 , 2001, 14 (4) : 377-384 WANG Feiyue. Computing with words and a framework for computational linguistic dynamic systems[J]. Pattern Recognition and Artificial Intelligence , 2001, 14 (4) : 377-384 [3] WANG F Y. On the abstraction of conventional dynamic systems: from numerical analysis to linguistic analysis[J]. Information Sciences , 2005, 171 (1/2/3) : 233-259 [4] WANG F Y, YANG T, MO H. On fixed points of linguistic dynamic systems[J]. Journal of System Simulation , 2002, 14 (11) : 1479-1485 [5] 王飞跃. 词计算和语言动力学系统的基本问题和研究[J]. 自动化学报 , 2005 (6) : 32-40 WANG Feiyue. Fundamental issues in research of computing with words and linguistic dynamic systems[J]. Acta Automatica Sinica , 2005 (6) : 32-40 [6] 莫红, 王飞跃. 基于词计算的语言动力系统及其稳定性[J]. 中国科学: F辑 , 2009, 39 (2) : 254-268 [7] PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Sciences , 1982, 11 (5) : 341-356 DOI:10.1007/BF01001956 [8] PAWLAK Z. Rough Sets: Theoretical aspects of reasoning about data[M]. Boston: Kluwer Academic Publishers, 1991 : 1 -79. [9] ZAKOWSKI W. Approximations in the space(U,∏)[J]. Demonstratio Mathematica , 1983 (16) : 761-769 [10] ZHU W, WANG F. Reduction and axiomization of covering generalized rough sets[J]. Information Sciences , 2003, 152 : 217-230 DOI:10.1016/S0020-0255(03)00056-2 [11] ZHU W,WANG F. Axiomatic systems of generalized rough sets[C]//Proceedings of the 1st International Conference on Rough Sets and Knowledge Technology. Chongqing,China,2006: 216-221. [12] ZHU W,WANG F. Covering based granular computing for conflict analysis[C]//IEEE International Conference on Intelligence and Security Informatics. San Diego,CA,USA: 2006: 566-571. [13] ZHU W,WANG F. Relationships among three types of covering rough sets[C]//IEEE International Conference on Granular Computing. Atlanta,GA,USA,2006: 43-48. [14] ZHU W,WANG F. Topological properties in covering-based rough sets[C]//Proceedings of the 4th International Conference on Fuzzy Systems and Knowledge Discovery. Haikou,China,2007: 289-293. [15] ZHU W, WANG F. On three types of covering-based rough sets[J]. IEEE Transactions on Knowledge and Data Engineering , 2007, 19 (8) : 1131-1143 DOI:10.1109/TKDE.2007.1044 [16] ZHU W, WANG F. The fourth type of covering-based rough sets[J]. Information Sciences , 2012, 201 : 80-92 DOI:10.1016/j.ins.2012.01.026 [17] YAO Y Y, YAO B X. Covering based rough set approximations[J]. Information Sciences , 2012, 200 : 91-107 DOI:10.1016/j.ins.2012.02.065 [18] GE X, BAI X L, YUN Z Q. Topological characterizations of covering for special covering-based upper approximation operators[J]. Information Sciences , 2012, 204 : 70-81 DOI:10.1016/j.ins.2012.04.005 [19] WANG L J, YANG X B, YANG J Y, et al. Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system[J]. Information Sciences , 2012, 207 (10) : 66-78 [20] TANG J G, SHE K, WANG Y Q. Covering-based soft rough sets[J]. Journal of Electronic Science and Technology , 2011, 9 (2) : 118-123 [21] TANG J G,SHE K,ZHU W. The refinement in covering-based rough sets[C]//Proceedings of the International Conference on Granular Computing. Taipei,China,2011: 641-646. [22] TANG J G, SHE K, ZHU W. Covering-based rough sets based on the refinement of covering-element[J]. International Journal of Computational and Mathematical Sciences , 2011, 5 : 198-208 [23] WANG S P, ZHU W. Matroidal structure of covering-based rough sets through the upper approximation number[J]. International Journal of Granular Computing,Rough Sets and Intelligent Systems , 2011, 2 (2) : 141-148 DOI:10.1504/IJGCRSIS.2011.043369 [24] ZHANG Y, LI J, WU W. On axiomatic characterizations of three pairs of covering based approximation operators[J]. Information Sciences , 2010, 180 (2) : 274-287 DOI:10.1016/j.ins.2009.08.031
DOI: 10.3969/j.issn.1673-4785.201307018

0

#### 文章信息

TANG Jianguo, WANG Jianghua, HAN Liying, ZHU Feng

Linguistic dynamic systems based on covering-based rough sets

CAAI Transactions on Intelligent Systems, 2014, 9(2): 229-234
http://dx.doi.org/10.3969/j.issn.1673-4785.201307018