Interval Type-2 Fuzzy Rough Sets Based on Inclusion Measures
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摘要: 基于区间二型模糊包含度的公理化定义,给出了新的区间二型模糊包含度计算公式.进一步,通过包含度定义了区间二型模糊粗糙集,并讨论了它的一些基本性质.最后,利用区间二型模糊粗糙集研究了连续域决策信息系统的属性约简,给出了新的约简方法.实例说明了该约简方法的具体计算步骤,并且通过实验验证了该算法的有效性和可行性.Abstract: In this paper, a new computation formula of interval type-2 fuzzy inclusion measure is proposed on the basis of the axiom definition of interval type-2 fuzzy inclusion measures. Furthermore, we define an interval type-2 fuzzy rough set model on the basis of inclusion measure and study its basic properties. In the end, the attribute reduction of continuous domain decision information system is discussed and the method on appropriate reduction is given. Further, we present calculation steps of the reduction approach by an example and experimental results demonstrate the feasibility and effectiveness of the reduction algorithm.
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[1] Zadeh L A. Fuzzy sets. Information and Control, 1965, 8(3): 338-356 [2] Zadeh L A. The concept of linguistic variable and its application to approximate reasoning. Information Sciences, 1975, 8(3): 199-249 [3] Yang M S, Lin D C. On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering. Computer and Mathematics with Applications, 2009, 57(6): 896-907 [4] Hwang C M, Yang M S, Hung W L, Lee E S. Similarity, inclusion and entropy measures between type-2 fuzzy sets based on the Sugeno integral. Mathematical and Computer Modelling, 2011, 53(9-10): 1788-1797 [5] Pawlak Z. Rough sets. International Journal of Computer and Information Science, 1982, 11(5): 341-356 [6] Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning About Data. Boston: Kluwer Academic Publishers, 1991 [7] Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems, 1990, 17(2-3): 191-209 [8] Atanassov K T. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1986, 20(1): 87-96 [9] Atanassov K T. Intuitionistic Fuzzy Sets: Theory and Applications. Heidelberg: Physical-Verlag, 1999 [10] Cornelis C, De Cock M, Kerre E E. Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge. Expert Systems, 2003, 20(5): 260-270 [11] Xu Xiao-Lai, Lei Ying-Jie, Tan Qiao-Ying. Intuitionistic fuzzy rough sets based on triangle norm. Control and Decision, 2008, 23(8): 900-904(徐小来, 雷英杰, 谭巧英. 基于直觉模糊三角模的直觉模糊粗糙集. 控制与决策, 2008, 23(8): 900-904) [12] Zhou L, Wu W Z. On generalized intuitionistic fuzzy rough approximation operators. Information Sciences, 2008, 178(11): 2448-2465 [13] Zhou L, Wu W Z, Zhang W X. On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators. Information Sciences, 2009, 179(7): 883-898 [14] Lu Yan-Li, Lei Ying-Jie, Hua Ji-Xue. Attribute reduction based on intuitionistic fuzzy rough set. Control and Decision, 2009, 24(3): 335-341(路艳丽, 雷英杰, 华继学. 基于直觉模糊粗糙集的属性约简. 控制与决策, 2009, 24(3): 335-341) [15] Zhang Zhi-Ming, Bai Yun-Chao, Tian Jing-Feng. Intuitionistic fuzzy rough sets based on intuitionistic fuzzy coverings. Control and Decision, 2010, 25(9): 1369-1373(张植明, 白云超, 田景峰. 基于覆盖的直觉模糊粗糙集. 控制与决策, 2010, 25(9): 1369-1373) [16] Wu Hao-Yang, Wu Yu-Yuan, Luo Jing-Ping. An interval type-2 fuzzy rough set model for attribute reduction. IEEE Transactions on Fuzzy Systems, 2009, 17(2): 301-315 [17] Mendel J M. Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Upper Saddle River, NJ: Prentice Hall, 2001 [18] Jensen R, Shen Q. Fuzzy-rough attribute reduction with application to web categorization. Fuzzy Sets and Systems, 2004, 141(3): 469-485 [19] Bhatt R B, Copal M. On fuzzy-rough sets approach to feature selection. Pattern Recognition Letters, 2005, 26(7): 965-975 [20] Pan Yong-Ping, Huang Dao-Ping, Sun Zong-Hai. Overview of type-2 fuzzy logic control. Control Theory & Applications, 2011, 28(1): 13-23(潘永平, 黄道平, 孙宗海. II型模糊控制综述. 控制理论与应用, 2011, 28(1): 13-23)
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