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| 模糊粗糙近似算子公理集的独立性 | |
| 引用本文： | 齐晓东,尚馥娟,米据生.模糊粗糙近似算子公理集的独立性[J].模糊系统与数学,2006,20(4):97-104. |
| 作者姓名： | 齐晓东 尚馥娟 米据生 |
| 作者单位： | 1. 河北交通职业技术学院,河北,石家庄,050091 2. 河北行政学院,河北,石家庄,050031 3. 河北师范大学,数学与信息科学学院,河北,石家庄,050016 |
| 基金项目： | 河北省自然科学基金资助项目(A2006000129)，河北师范大学重点资助项目(L2005C01) |
| 摘 要： | 用双论域上的模糊关系定义了广义模糊粗糙近似算子,并讨论了近似算子的性质。用公理刻画了模糊集合值算子,各种公理化的近似算子可以保证找到相应的二元模糊关系,使得由模糊关系通过构造性方法定义的模糊粗糙近似算子恰好就是用公理定义的近似算子。讨论了刻画各种特殊近似算子的公理集的独立性,从而给出各种特殊模糊关系所对应的模糊粗糙近似算子的最小公理集。 |
| 关 键 词： | 粗糙集 模糊集 近似算子 公理化 |
| 文章编号： | 1001-7402（2006）04-0097-08 |
| 收稿时间： | 2005-10-27 |
| 修稿时间： | 2005-10-27 |
The Independence of the Axioms Characterizing Fuzzy Rough Approximation Operators |
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| QI Xiao-dong,SHANG Fu-juan,MI Jus-heng.The Independence of the Axioms Characterizing Fuzzy Rough Approximation Operators[J].Fuzzy Systems and Mathematics,2006,20(4):97-104. | |
| Authors: | QI Xiao-dong SHANG Fu-juan MI Jus-heng |
| Institution: | 1. Hebei Jiaotong Vocational Technical College,Shijiazhuang 050091 ,China; 2. Hebei College of Administration,Shijiazhuang 050031,China;3. College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang 050016,China |
| Abstract: | In the constructive approach,one starts from a fuzzy relation on two universes of discourse and defines a pair of lower and upper fuzzy rough approximation operators.Different classes of rough fuzzy set algebras are obtained from different types of fuzzy relations.The properties of the approximation operators are also discussed.In the axiomatic approach,one defines a pair of(dual) fuzzy rough approximation operators.Various classes of fuzzy rough algebras are characterized by(different) sets of axioms.Axioms of fuzzy rough approximation operators guarantee the existence of certain types of fuzzy relations producing the same fuzzy rough operators.The independence of the axioms characterizing fuzzy rough approximation operators is examined,and then the minimal sets of axioms for various fuzzy rough approximation operators are presented. |
| Keywords: | Rough Sets Fuzzy Sets Lower and Upper Approximation Operators Axioms |
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