[1]王金英,韩晓冰,王艳平.二型直觉模糊粗糙集[J].智能系统学报编辑部,2015,10(6):943-948.[doi:10.11992/tis.201412013]
WANG Jinying,HAN Xiaobing,WANG Yanping.Type-2 intuitionistic fuzzy rough sets[J].CAAI Transactions on Intelligent Systems,2015,10(6):943-948.[doi:10.11992/tis.201412013]
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WANG Jinying,HAN Xiaobing,WANG Yanping.Type-2 intuitionistic fuzzy rough sets[J].CAAI Transactions on Intelligent Systems,2015,10(6):943-948.[doi:10.11992/tis.201412013]
二型直觉模糊粗糙集
《智能系统学报》编辑部[ISSN 1673-4785/CN 23-1538/TP] 卷:
10
期数:
2015年第6期
页码:
943-948
栏目:
学术论文—知识工程
出版日期:
2015-12-25
- Title:
- Type-2 intuitionistic fuzzy rough sets
- Keywords:
- intuitionistic fuzzy sets; rough sets; type-2 fuzzy sets; type-2 intuitionistic fuzzy sets; type-2 intuitionistic fuzzy rough sets; approximation operators
- 分类号:
- TP301;O236
- 摘要:
- 将二型直觉模糊集和粗糙集理论融合,建立二型直觉模糊粗糙集模型。首先,在二型直觉模糊近似空间中,定义了一对二型直觉模糊上、下近似算子,并讨论了二型直觉模糊关系退化为普通二型模糊关系和一般等价关系时,上、下近似算子的具体变化形式。然后,将普通二型模糊集之间包含关系的定义推广到了二型直觉模糊集,在此基础上研究了二型直觉模糊上、下近似算子的一些性质。最后,定义了自反的、对称的和传递的二型直觉模糊关系,并讨论了这3种特殊的二型直觉模糊关系与近似算子的特征之间的联系。该结论进一步丰富了二型模糊集理论和粗糙集理论,为二型直觉模糊信息系统的应用奠定了良好的理论基础。
- Abstract:
- In this study, we integrate the theories of type-2 intuitionistic fuzzy sets and rough sets to construct a type-2-intuitionistic-fuzzy-and-rough-sets model. First, in type-2 intuitionistic fuzzy approximation space, we define a pair of type-2 intuitionistic fuzzy upper and lower approximation operators. We then discuss specific changes in these upper and lower approximation operators for a situation in which the type-2 intuitionistic fuzzy relations degenerate into common type-2-fuzzy and general-equivalence relations. Next, we generalize the definition of the inclusion relation between general type-2 fuzzy sets as type-2 intuitionistic fuzzy sets. On this basis, we then explored the properties of type-2-intuitionistic-fuzzy upper and lower approximation operators. We then defined reflexive, symmetric, and transitive type-2 intuitionistic fuzzy relations. Finally, we discuss the relations between these three special type-2 intuitionistic fuzzy relations and the characteristics of their approximation operators. Conclusions drawn in this study further enrich the theories of type-2 intuitionistic fuzzy and rough sets and establish a good theoretical basis for the application of the type-2 intuitionistic fuzzy information system.
- 参考文献/References:
-
[1] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-353.
[2] ATANASSOV K T. Intuitionstic fuzzy sets[J]. Fuzzy Sets and Systems, 1986, 20(1):87-96.
[3] ATANASSOV K T, GARGOV G. Interval valued intuitionstic fuzzy sets[J]. Fuzzy Sets and Systems, 1989, 31(3):343-349.
[4] ZADEH L A. The concept of a linguistic variable and its application to approximate reasoning[J]. Information Science, 1975, 8(3):199-249.
[5] MENDEL J M, JOHN R I B. Type-2 fuzzy sets made simple[J]. IEEE Transactions on Fuzzy Systems, 2002, 10(2):117-127.
[6] PAWLAK Z. Rough sets[J]. International Journal of Computer & Information Sciences, 1982, 11(5):341-356.
[7] DUBOIS D, PRADE H. Rough fuzzy sets and fuzzy rough sets[J]. International Journal of General Systems, 1990, 17(2-3):191-209.
[8] CORNELIS C, DE COCK M, KERRE E E. Intuitionistic fuzzy rough sets:at the crossroads of imperfect knowledge[J]. Expert Systems, 2003, 20(5):260-270.
[9] ZHOU Lei, WU Weizhi. On generalized intuitionistic fuzzy rough approximation operators[J]. Information Sciences, 2008, 178(11):2448-2465.
[10] 赵涛, 肖建. 二型模糊粗糙集[J]. 控制与决策, 2013, 28(3):385-390. ZHAO Tao, XIAO Jian. Type-2 fuzzy rough sets[J]. Control and Decision, 2013, 28(3):385-390.
[11] 赵涛, 肖建. 二型直觉模糊集[J]. 控制理论与应用, 2012, 29(9):1215-1222. ZHAO Tao, XIAO Jian. Type-2 intuitionistic fuzzy sets[J]. Control Theory & Applications, 2012, 29(9):1215-1222.
[12] KARNIK N N, MENDEL J M. Operations on type-2 fuzzy sets[J]. Fuzzy Sets and Systems, 2001, 122(2):327-348.
[13] MIZUMOTO M, TANAKA K. Some properties of fuzzy sets of type2[J]. Information and Control, 1976, 31(4):312-340.
[14] 邓廷权, 王占江, 汪培培, 等. 二型模糊集的模糊熵研究[J]. 控制与决策, 2012, 27(3):408-412. DENG Tingquan, WANG Zhanjiang, WANG Peipei, et al. Study on fuzzy entropy of type-2 fuzzy sets[J]. Control and Decision, 2012, 27(3):408-412.
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备注/Memo
收稿日期:2014-12-15;改回日期:。
基金项目:辽宁省教育厅基金资助项目(L2012226).
作者简介:王金英,女,1981年生,讲师,主要研究方向为粗糙集理论、模糊集理论。韩晓冰,女,1988年生,研究生,主要研究方向为粗糙集理论与应用。王艳平,女,1965年生,教授,主要研究方向为粗糙集理论、模糊集理论。发表学术论文30余篇。
通讯作者:王金英.E-mail:ying2000_2004@163.com.
更新日期/Last Update:
1900-01-01