多粒度覆盖粗糙直觉模糊集模型
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摘要
多粒度粗糙集是粗糙集模型在多粒度及分布式环境中的一种重要拓展形式,而覆盖粗糙直觉模糊集是处理不确定性问题的一种有效方法.为了更有效的处理不确定性问题,将多粒度粗糙集与覆盖粗糙直觉模糊集结合,建立了多粒度覆盖粗糙直觉模糊集模型,并给出了该模型下的一些性质;同时提出了多粒度覆盖粗糙直觉模糊集的模糊度的概念,讨论了其不确定性度量;最后给出了算例.
Exploring rough sets from the perspective of multi-granulation represents a promising direction in rough set theory,where concepts are approximated by multiple granular structures represented by binary relations.While covering rough-intuitionistic fuzzy sets provide an effective method to deal with the uncertainty in data.Through a combination of multi-granulation rough set with covering rough-intuitionistic fuzzy set,we construct a new multi-granulation rough set model,called a multi-granulation covering rough-intuitionistic fuzzy set model,which can be applied to deal with uncertainty more effectively.Then we present some properties,such as monotonicity,duality property and so on,which are similar to those of the classical rough set.We also introduce the concept of fuzziness to describe the uncertainty of this model.Finally,we examine our approach with a detailed example.
Exploring rough sets from the perspective of multi-granulation represents a promising direction in rough set theory,where concepts are approximated by multiple granular structures represented by binary relations.While covering rough-intuitionistic fuzzy sets provide an effective method to deal with the uncertainty in data.Through a combination of multi-granulation rough set with covering rough-intuitionistic fuzzy set,we construct a new multi-granulation rough set model,called a multi-granulation covering rough-intuitionistic fuzzy set model,which can be applied to deal with uncertainty more effectively.Then we present some properties,such as monotonicity,duality property and so on,which are similar to those of the classical rough set.We also introduce the concept of fuzziness to describe the uncertainty of this model.Finally,we examine our approach with a detailed example.
引文
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[4]周国静,李云.基于最小最大策略的集成特征选择.南京大学学报(自然科学),2014,50(4):457~465.
[5]徐健锋,张远健,Zhou D N等.基于粒计算的不确定性时间序列建模及其聚类.南京大学学报(自然科学),2014,50(1):86~94.
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[9]Zhu W,Wang F Y.Reduction and axiomization of covering generalized rough sets.Information Science,2003,152(1):217~230.
[10]Bonikowski Z,Bryniarski E,Wybraniec-skardowska U.Extensions and intentions in the rough set theory.Information Science,1998,107(1):149~167.
[11]Atanassov K.Intuitionistic fuzzy sets.Fuzzy Sets and Systems,1986,20(1):87~96.
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[13]Qian Y H,Liang J Y,Dang C Y.Incomplete multigranulation rough set.IEEE Transactions on Systems,Man and Cybernetics,Part A,2010(20):420~431.
[14]Qian Y H,Liang J Y,Yao Y Y,et al.MGRS:A multi-granulation rough set.Information Sciences,2010,180(6):949~970.
[15]Zhao S Y,Tsang E C,Chen D G.The model of fuzzy variable precision rough sets.IEEE Transactions on Fuzzy Systems,2009,17:451~467.
[16]Inuiguchi M,Yoshioka Y,Kusunoki Y.Variableprecision dominance-based rough set approach and attribute reduction.International Journal of Approximate Reasoning,2009,50:1199~1214.
[17]王金英.粗糙直觉模糊集的不确定性分析.辽宁工业大学学报,2013,33(6):403~406.
[18]吕印超,郭嗣琮.直觉模糊集的熵及其一般形式.计算机工程与应用,2011,47(28):52~55.
[2]李飞江,成红红,钱宇华.全粒度聚类算法.南京大学学报(自然科学),2013,50(4):553~560.
[3]李同军,王霞,徐优红.形式概念的布尔计算方法.南京大学学报(自然科学),2014,49(5):505~516.
[4]周国静,李云.基于最小最大策略的集成特征选择.南京大学学报(自然科学),2014,50(4):457~465.
[5]徐健锋,张远健,Zhou D N等.基于粒计算的不确定性时间序列建模及其聚类.南京大学学报(自然科学),2014,50(1):86~94.
[6]Atanassov K.Intuitionistic fuzzy sets.Fuzzy sets and Systems,1986,20(1):87~96.
[7]朱六兵,王迪焕.粗糙Vague集及其相似性度量.模糊系统与数学,2006,20(6):130~134.
[8]巩增泰,马延.覆盖粗糙直觉模糊集模型.计算机工程与应用,2010,46(3):42~45.
[9]Zhu W,Wang F Y.Reduction and axiomization of covering generalized rough sets.Information Science,2003,152(1):217~230.
[10]Bonikowski Z,Bryniarski E,Wybraniec-skardowska U.Extensions and intentions in the rough set theory.Information Science,1998,107(1):149~167.
[11]Atanassov K.Intuitionistic fuzzy sets.Fuzzy Sets and Systems,1986,20(1):87~96.
[12]Atanassov K.Operators over interval valued intuitionistic fuzzy sets.Fuzzy Sets and Systems,1994,64:159~174.
[13]Qian Y H,Liang J Y,Dang C Y.Incomplete multigranulation rough set.IEEE Transactions on Systems,Man and Cybernetics,Part A,2010(20):420~431.
[14]Qian Y H,Liang J Y,Yao Y Y,et al.MGRS:A multi-granulation rough set.Information Sciences,2010,180(6):949~970.
[15]Zhao S Y,Tsang E C,Chen D G.The model of fuzzy variable precision rough sets.IEEE Transactions on Fuzzy Systems,2009,17:451~467.
[16]Inuiguchi M,Yoshioka Y,Kusunoki Y.Variableprecision dominance-based rough set approach and attribute reduction.International Journal of Approximate Reasoning,2009,50:1199~1214.
[17]王金英.粗糙直觉模糊集的不确定性分析.辽宁工业大学学报,2013,33(6):403~406.
[18]吕印超,郭嗣琮.直觉模糊集的熵及其一般形式.计算机工程与应用,2011,47(28):52~55.