覆盖变精度粗糙模糊集模型
|
摘要
在研究覆盖粗糙集模型的基础上,凭借所提出的对象最小描述邻域对于一个特定模糊集的相对错误分类率,考虑对象最小描述的近邻域、邻域、规则置信度和元素隶属度4种覆盖,定义并建立了4种类型的覆盖变精度粗糙模糊集模型,讨论了其性质和相互关系,推广和统一了已有的结果,并给出了算例.
Based on the discussion of the covering rough set models and the minimum description neighborhood of elements for the relative error classification rate of a given fuzzy set proposed in this paper,four kinds of covering variable precision rough fuzzy set models were defined and established by means of a minimum description of the neighbor domain, whole neighborhood, rule confidence and membership of the elements, unifying the results of predecessors. Their properties and relationships were discussed,an example was given.
Based on the discussion of the covering rough set models and the minimum description neighborhood of elements for the relative error classification rate of a given fuzzy set proposed in this paper,four kinds of covering variable precision rough fuzzy set models were defined and established by means of a minimum description of the neighbor domain, whole neighborhood, rule confidence and membership of the elements, unifying the results of predecessors. Their properties and relationships were discussed,an example was given.
引文
[1] Pawlak Z. Rough set[J]. International Journal of Computer and Information Science, 1982, 11(5):341-356.
[2] Ziarko W. Variable precision rough set model[J]. Journal of Computer and System Science, 1993, 46(1):39-59.
[3] Zakoski W. Approximotions in the space(U,Π)[J]. Demonstratio Mathematica, 1983, 16(3):761-769.
[4] Bonikowski Z, Bryniarski E, Wybraniec U. Extensions and intentions in the rough set theory[J]. Information Sciences, 1998, 107(1):149-167.
[5] Zhu W, Wang Fei-yue. Reduction and axiomization of covering generalized rough sets[J]. Information Sciences,2003, 152:217-230.
[6] Xu Wei-hua, Zhang Wen-xiu. Measuring roughness of generalized rough sets induced by a covering[J]. Fuzzy Sets and Systems, 2007, 158(22):2443-2455.
[7] Chen De-guang, Wang Chang-zhong, Hu Qing-hua. A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets[J]. Information Science, 2007, 177(17):3500-3518.
[8] Zhu W. Topological approaches to covering rough sets[J].Information Sciences, 2006, 177(6):1499-1508.
[9] Zhu W. Relationship between generalized rough sets based on binary relation and covering[J]. Information Sciences, 2008, 179(3):210-225.
[10] Zhu W. Relationship among basic concepts in coveringbased rough sets[J]. Information Sciences, 2009, 179(14):2478-2486.
[11] Zhu W, Wang Fei-yue. The fourth type of covering-based rough sets[J]. Information Sciences, 2012, 201(6):80-92.
[12] Gong Zeng-tai, Chai Run-li. Covering multigranulation trapezoidal fuzzydecision-theoretic rough fuzzy set models and applications[J]. Journal of Intelligent and Fuzzy Systems, 2016, 31(3):1621-1633.
[13] Shi Zhan-hong, Gong Zeng-tai. The further investigation of covering-based rough sets:uncertainty characterization, similarity measure and generalized models[J].Information Sciences, 2010, 180(19):3745-3763.
[14]徐伟华,张文修.覆盖广义粗糙集的模糊性[J].模糊系统与数学, 2006, 20(6):115-121.
[15]胡军,王国胤,张清华.一种覆盖模糊集模型[J].软件学报, 2010, 21(5):968-977.
[16]连玉平,刘坤,史战红.一种由三角模所诱导的粗糙集间的相似性度量方法[J].兰州大学学报:自然科学版,2014, 50(4):552-555.
[17]巩增泰,赵伟.基于对偶三角模的直觉模糊粗糙集模型[J].兰州大学学报:自然科学版, 2011, 47(6):84-92.
[18]巩增泰,雷文婧.基于σ-λ律非可加测度的移动加权平均方法[J].兰州大学学报:自然科学版, 2016, 52(5):686-691.
[19]徐忠印,廖家齐.基于覆盖的模糊粗糙集模型[J].模糊系统与数学, 2006, 20(3):141-144.
[20]魏莱,苗夺谦,徐菲菲,等.基于覆盖的粗糙模糊集模型研究[J].计算机研究与发展, 2006, 43(10):1719-1723.
[21]汤建国,余堃,祝峰.一种新的覆盖粗糙模糊集模型[J].控制与决策, 2012, 27(11):1053-1662.
[22]巩增泰,孙秉珍,邵亚斌,等.一般关系下的变精度粗糙集模型[J].兰州大学学报:自然科学版, 2005, 41(6):110-114.
[23]吴从炘,马明.模糊分析学基础[M].北京:国防工业出版社, 1991:2-10.
[24]刘瑞新,孙士保,秦克云.变精度覆盖粗糙集[J].计算机科学与应用, 2008, 44(12):47-50.
[25]孙士保,刘瑞新,秦克云.变精度粗糙模糊集模型研究[J].计算机工程与应用, 2007, 43(23):15-17.
[26] Dubois D, Prade H. Putting rough sets and fuzzy sets together[M]//Handbook of Application and Advance of the Rough Sets Theory, Boston:Kluwer Academic Publishers, 1992:203-222.
[27] Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets[J]. Journal of General Systems, 1990, 17(3/4):191-208.
[2] Ziarko W. Variable precision rough set model[J]. Journal of Computer and System Science, 1993, 46(1):39-59.
[3] Zakoski W. Approximotions in the space(U,Π)[J]. Demonstratio Mathematica, 1983, 16(3):761-769.
[4] Bonikowski Z, Bryniarski E, Wybraniec U. Extensions and intentions in the rough set theory[J]. Information Sciences, 1998, 107(1):149-167.
[5] Zhu W, Wang Fei-yue. Reduction and axiomization of covering generalized rough sets[J]. Information Sciences,2003, 152:217-230.
[6] Xu Wei-hua, Zhang Wen-xiu. Measuring roughness of generalized rough sets induced by a covering[J]. Fuzzy Sets and Systems, 2007, 158(22):2443-2455.
[7] Chen De-guang, Wang Chang-zhong, Hu Qing-hua. A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets[J]. Information Science, 2007, 177(17):3500-3518.
[8] Zhu W. Topological approaches to covering rough sets[J].Information Sciences, 2006, 177(6):1499-1508.
[9] Zhu W. Relationship between generalized rough sets based on binary relation and covering[J]. Information Sciences, 2008, 179(3):210-225.
[10] Zhu W. Relationship among basic concepts in coveringbased rough sets[J]. Information Sciences, 2009, 179(14):2478-2486.
[11] Zhu W, Wang Fei-yue. The fourth type of covering-based rough sets[J]. Information Sciences, 2012, 201(6):80-92.
[12] Gong Zeng-tai, Chai Run-li. Covering multigranulation trapezoidal fuzzydecision-theoretic rough fuzzy set models and applications[J]. Journal of Intelligent and Fuzzy Systems, 2016, 31(3):1621-1633.
[13] Shi Zhan-hong, Gong Zeng-tai. The further investigation of covering-based rough sets:uncertainty characterization, similarity measure and generalized models[J].Information Sciences, 2010, 180(19):3745-3763.
[14]徐伟华,张文修.覆盖广义粗糙集的模糊性[J].模糊系统与数学, 2006, 20(6):115-121.
[15]胡军,王国胤,张清华.一种覆盖模糊集模型[J].软件学报, 2010, 21(5):968-977.
[16]连玉平,刘坤,史战红.一种由三角模所诱导的粗糙集间的相似性度量方法[J].兰州大学学报:自然科学版,2014, 50(4):552-555.
[17]巩增泰,赵伟.基于对偶三角模的直觉模糊粗糙集模型[J].兰州大学学报:自然科学版, 2011, 47(6):84-92.
[18]巩增泰,雷文婧.基于σ-λ律非可加测度的移动加权平均方法[J].兰州大学学报:自然科学版, 2016, 52(5):686-691.
[19]徐忠印,廖家齐.基于覆盖的模糊粗糙集模型[J].模糊系统与数学, 2006, 20(3):141-144.
[20]魏莱,苗夺谦,徐菲菲,等.基于覆盖的粗糙模糊集模型研究[J].计算机研究与发展, 2006, 43(10):1719-1723.
[21]汤建国,余堃,祝峰.一种新的覆盖粗糙模糊集模型[J].控制与决策, 2012, 27(11):1053-1662.
[22]巩增泰,孙秉珍,邵亚斌,等.一般关系下的变精度粗糙集模型[J].兰州大学学报:自然科学版, 2005, 41(6):110-114.
[23]吴从炘,马明.模糊分析学基础[M].北京:国防工业出版社, 1991:2-10.
[24]刘瑞新,孙士保,秦克云.变精度覆盖粗糙集[J].计算机科学与应用, 2008, 44(12):47-50.
[25]孙士保,刘瑞新,秦克云.变精度粗糙模糊集模型研究[J].计算机工程与应用, 2007, 43(23):15-17.
[26] Dubois D, Prade H. Putting rough sets and fuzzy sets together[M]//Handbook of Application and Advance of the Rough Sets Theory, Boston:Kluwer Academic Publishers, 1992:203-222.
[27] Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets[J]. Journal of General Systems, 1990, 17(3/4):191-208.