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。
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 of their 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.
作者
杨洁
王国胤
张清华
冯林
YANG Jie;WANG Guo-yin;ZHANG Qing-hua;FENG Lin(Chongqing Key Laboratory of Computational Intelligence,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;School of Physics and Electronic,Zunyi Normal University,Zunyi,Guizhou 563002,China;School of Computer Science,Sichuan Normal University,Chengdu 610000,China)
出处
《计算机科学》
CSCD
北大核心
2019年第1期45-50,共6页
Computer Science
基金
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[2017]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
关键词
粗糙模糊集
不确定性度量
模糊度
层次粒结构
Rough fuzzy sets
Uncertainty measure
Fuzziness
Hierarchical granular structure
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;通信作者: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;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。
