层次粒结构下粗糙模糊集的不确定性度量

doi:10.11896／j.issn.1002-137X.2019.01.007

计算机科学 ›› 2019, Vol. 46 ›› Issue (1): 45-50.doi: 10.11896／j.issn.1002-137X.2019.01.007

• 2018 年第七届中国数据挖掘会议 • 上一篇下一篇

层次粒结构下粗糙模糊集的不确定性度量

杨洁^1,2, 王国胤¹, 张清华¹, 冯林³

(重庆邮电大学计算智能重庆市重点实验室重庆400065)¹
(遵义师范学院物理与电子科学学院贵州遵义563002)²
(四川师范大学计算机科学学院成都610000)³

收稿日期:2018-06-10 出版日期:2019-01-15 发布日期:2019-02-25
作者简介:杨洁(1987－),男,博士生,副教授,主要研究方向为粗糙集、粒计算、机器学习;王国胤(1970－),男,博士,教授,CCF杰出会员,主要研究方向为粗糙集、粒计算、认知计算、智能信息处理、数据挖掘,E-mail:wanggy@ieee.org(通信作者);张清华(1974－),男,博士,教授,主要研究方向为粗糙集、粒计算;冯林(1972－),男,博士,教授,主要研究方向为粗糙集、粒计算。
基金资助:
国家自然科学基金(61572091,61472056,61772096),高端人才项目(RC2016005),贵州省联合基金项目(黔科合LH字7075号),贵州省教育厅青年科技人才成长项目(黔教合KY字[2018]318号)资助

Uncertainty Measure of Rough Fuzzy Sets in Hierarchical Granular Structure

YANG Jie^1,2, WANG Guo-yin¹, ZHANG Qing-hua¹, FENG Lin³

(Chongqing Key Laboratory of Computational Intelligence,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)¹
(School of Physics and Electronic,Zunyi Normal University,Zunyi,Guizhou 563002,China)²
(School of Computer Science,Sichuan Normal University,Chengdu 610000,China)³

Received:2018-06-10 Online:2019-01-15 Published:2019-02-25

摘要/Abstract

摘要： 众所周知,经典粗糙集的不确定性来自于边界域,但是对于粗糙模糊集来说,其正域和负域中的元素存在不确定性,从而导致粗糙模糊集的不确定性不仅来自于边界域,还来自于正域和负域。另外,在粗糙模糊集中,一个模糊概念可以通过层次粒结构中不同的粗糙近似空间进行刻画,随着粒度的变化,模糊概念的不确定性的变化规律如何？对此,文中提出一种基于模糊度的不确定性度量公式,并基于均值模糊集分析了粗糙模糊集模型,得出粗糙模糊集不确定性度量的模型同样适合于度量概率粗糙集的不确定性的结论。其次,采用基于模糊度的不确定性度量方法,揭示了分层递阶的多粒度空间下粗糙模糊集不确定性的变化规律。然后,分析了3个域(正域、边界域和负域)的不确定性,并揭示了它们在分层递阶的多粒度空间下的变化规律。最后,通过实验验证了所提不确定性度量理论的有效性。

关键词: 不确定性度量, 层次粒结构, 粗糙模糊集, 模糊度

Abstract: There has been a consensus that the uncertainty of Pawlak’s rough sets model is rooted in the objects contained in the boundary region of the target concept,while the uncertainty of rough fuzzy sets results from three regions,because the objects in the positive or negative regions are probably uncertain.Moreover,in rough fuzzy sets model,a fuzzy concept can be characterized by different rough approximation spaces in a hierarchical granular structure,so how will the uncertainty of a fuzzy concept change with granularity? This paper firstly proposed a fuzziness-based uncertainty measure,analyzed the rough fuzzy set model through the average fuzzy sets and drew a conclusion,that is the uncertainty measure for rough fuzzy sets is also suitable for probabilistic rough sets.Based on the fuzziness-based uncertainty measure,this paper revealed the change rules oftheir uncertainty of rough fuzzy sets in a hierarchical granular structure.Then,it discussed the uncertainties of the three regions (positive region,boundary region and negative region) and revealed the change rules of their uncertainty in a hierarchical granular structure.Finally,experimental results demonstrate the effectiveness of the proposed uncertainty measure theory.

Key words: Fuzziness, Hierarchical granular structure, Rough fuzzy sets, Uncertainty measure

中图分类号:

TP311

杨洁, 王国胤, 张清华, 冯林. 层次粒结构下粗糙模糊集的不确定性度量[J]. 计算机科学, 2019, 46(1): 45-50. https://doi.org/10.11896／j.issn.1002-137X.2019.01.007

YANG Jie, WANG Guo-yin, ZHANG Qing-hua, FENG Lin. Uncertainty Measure of Rough Fuzzy Sets in Hierarchical Granular Structure[J]. Computer Science, 2019, 46(1): 45-50. https://doi.org/10.11896／j.issn.1002-137X.2019.01.007

参考文献

[1]PAWLAK Z.Rough sets[J].International Journal of Computer Information Sciences,1982,11(5):341-356. [2]PAWLAK Z.Rough classification[J].International Journal of Man-Machine Studies,1984,20(5):469-483. [3]DUBOIS D,PRADE H.Rough fuzzy sets and fuzzy rough sets[J].International Journal of General System,1990,17(2-3):191-209. [4]DUBOIS D,PRADE H.Putting rough sets and fuzzy sets to- gether[M]//Słowin′ski R,Ed.Intelligent decision support:Handbook of applications and advances of the rough sets theory.Dordrecht:Kluwer Academic Publishers,1992:203-232. [5]DUBOIS D,PRADE H.Twofold fuzzy sets and rough sets－Some issues in knowledge representation[J].Fuzzy Sets & Systems,1987,23(1):3-18. [6]WIERMAN M J.Measureing uncertainty in rough set theory[J].International Journal of General Systems,1999,28(4-5):283-297. [7]LIANG J Y,CHIN K S,DANG C Y.A new method for measuring uncertainty and fuzziness in rough set theory[J].International Journal of General Systems,2002,31(4):331-342. [8]梁吉业,李德玉.信息系统中的不确定性与知识获取[M].北京:科学出版社,2005. [9]LIANG J Y,SHI Z Z.The information entropy,rough entropy and knowledge granulation in rough set theory[J].International Journal of Uncertainty,Fuzziness and Knowledge—Based Systems,2004,12(1):37-46. [10]QIAN Y H,CHENG H,WANG J,et al.Grouping granular structures in human granulation intelligence[J].Information Sciences,2017,382-383:150-169. [11]HU Q H,YU D,XIE Z,et al.Fuzzy probabilistic approximation spaces and their information measures[J].IEEE Transactions on Fuzzy Systems,2006,14(2):191-201. [12]ZHANG Q H,ZHANG Q,WANG G Y.The uncertainty of probabilistic rough sets in multi-granulation spaces[J].International Journal of Approximate Reasoning,2016,77:38-54. [13]ZHANG Q H,YANG S,WANG G Y.Measuring Uncertainty of Probabilistic Rough Set Model From Its Three Regions[J].IEEE Transactions on Systems Man & Cybernetics Systems,2016,PP(99):1-11. [14]WANG G Y,ZHANG Q H.Research on the uncertainty of rough sets under different knowledge granularity[J].Chinese Journal of Computers,2008,31(9):1588-1598.(in Chinese) 王国胤,张清华.不同知识粒度下粗糙集的不确定性研究[J].计算机学报,2008,31(9):1588-1598. [15]YAO Y Y,ZHAO L.A measurement theory view on the granularity of partitions[J].Information Sciences,2012,213(23):1-13. [16]GUO Z X,MI J S.An Uncertainty Measure in Rough Fuzzy Sets[J].Fuzzy Systems & Mathematics,2005,19(4):135-140.(in Chinese) 郭增晓,米据生.粗糙模糊集的模糊性度量[J].模糊系统与数学,2005,19(4):135-140. [17]QIN H N,LUO D R.New uncertainty measure of rough fuzzy sets and entropy weight method for fuzzy-target decision-making tables[J].Journal of Applied Mathematics,2014,42(6):1-7. [18]HU J,PEDRYCZ W,WANG G Y.A roughness measure of fuzzy sets from the perspective of distance[J].International Journal of General Systems,2016 (3):1-16. [19]SUN B Z,MA W M.Uncertainty measure for general relation-based rough fuzzy set[J].Kybernetes,2013,42(6):979-992. [20]PEDRYCZ W,SKOWRON A,KREINOVICH V.Handbook of Granular Computing [M].Wiley-Interscience,2008:719-740. [21]PEDRYCZ W,ALHMOUZ R,MORFEQ A,et al.The design of free structure granular mappings:the use of the principle of justifiable granularity[J].IEEE Transactions on Cybernetics,2013,43(6):2105-2113. [22]WANG G Y,YANG J,XU J.Granular computing:from granularity optimization to multi-granularity joint problem solving[J].Granular Computing,2017,2(3):1-16. [23]YAO Y Y.Perspectives of granular computing[C]//IEEE International Conference on Granular Computing.IEEE,2005:85-90. [24]李德毅,刘常昱,杜鹢,等.不确定性人工智能[M].北京:国防工业出版社,2005. [25]ZADEH L A.Fuzzy sets[J].Information & Control,1965, 8(3):338-353. [26]ZHANG B,ZHANG L.Theory and Applications of Problem Solving[M].Elsevier Science Inc.,1992. [27]LI D Y,MENG H J,SHI X M.Membership cloud and affiliated cloud generator[J].Journal of Computer Research and Development,1995,32 (6):15-20.(in Chinese) 李德毅,孟海军,史雪梅.隶属云和隶属云发生器[J].计算机研究与发展,1995,32(6):15-20. [28]STRASZECKA E.Combining uncertainty and imprecision in models of medical diagnosis[J].Information Sciences,2006,176(20):3026-3059. [29]DAI J,WANG W,XU Q.An Uncertainty Measure for Incomplete Decision Tables and Its Applications[J].IEEE Transactions on Cybernetics,2013,43(4):1277-1289. [30]YAGER R R.Decision makingunder measure-based granular uncertainty[J].Granular Computing,2018,3(4):345-353. [31]ZHANG Q H,WANG J,WANG G Y.Approximate representation of rough fuzzy sets[J].Chinese Journal of Computers,2015,38(7):1484-1496.(in Chinese) 张清华,王进,王国胤.粗糙模糊集的近似表示[J].计算机学报,2015,38(7):1484-1496. [32]CHAKRABARTY K,BISWAS R,NANDA S.Fuzziness in rough sets[J].Fuzzy Sets & Systems,2000,110(2):247-251. [33]Ucirvine machine learning repository[EB/OL].http://archive.ics.uci.edu/ml

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

层次粒结构下粗糙模糊集的不确定性度量

Uncertainty Measure of Rough Fuzzy Sets in Hierarchical Granular Structure

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 11

Metrics

本文评价

推荐阅读 0

[1]	杨洁,王国胤,李帅. 基于边界域的邻域知识距离度量模型 Neighborhood Knowledge Distance Measure Model Based on Boundary Regions 计算机科学, 2020, 47(3): 61-66. https://doi.org/10.11896/jsjkx.190500174
[2]	王斌,邵明文,王金鹤,张俊虎. 基于改进的优势关系下的不完备区间值信息系统评估模型 New Evaluation Model for Incomplete Interval-valued Information System Based on Improved Dominance Relations 计算机科学, 2014, 41(2): 253-256.
[3]	郑婷婷,朱凌云. 覆盖粗糙模糊集的不确定性研究 Uncertainty Measure Research on Rough Fuzzy Sets in Covering Approximation Space 计算机科学, 2014, 41(11): 252-255. https://doi.org/10.11896/j.issn.1002-137X.2014.11.048
[4]	周红琼,周宇,叶庆卫,王晓东. 基于IP应用的网络质量评价研究 Study of Network Quality Evaluation Based on IP Application 计算机科学, 2012, 39(Z6): 125-128.
[5]	解滨，李磊军，米据生. 基于知识粒度的粗糙集的不确定性度量 Uncertainty Measures of Rough Sets Based on Knowledge Granularities 计算机科学, 2010, 37(9): 225-228.
[6]	孙士保,吴庆涛,普杰信,秦克云. 基于广义变精度粗糙模糊集模型的知识发现 Knowledge Discovery Approach Based on Generalized Variable Precision Rough Fuzzy Set Model 计算机科学, 2009, 36(9): 157-160.
[7]	. 不完备模糊系统的优势关系粗糙集与知识约简计算机科学, 2009, 36(6): 192-195.
[8]	徐菲菲苗夺谦李道国魏莱. 基于覆盖的粗糙模糊集的粗糙熵计算机科学, 2006, 33(10): 179-181.
[9]	刘贵龙. 粗糙模糊集的格论性质计算机科学, 2003, 30(9): 83-84.
[10]	牟克典. 时态Dempster—Shafer理论计算机科学, 2003, 30(7): 4-6.
[11]	甘早斌陈正勇陈传波裴先登. SRS及其质量模糊度量方法的研究计算机科学, 2003, 30(4): 131-133.