| 基于MV-代数的度量型模糊粗糙集 |
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| 引用本文： | 熊兴国,路玲霞.基于MV-代数的度量型模糊粗糙集[J].山东大学学报(理学版),2019,54(11):81-89. |
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| 作者姓名： | 熊兴国 路玲霞 |
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| 作者单位： | 1.河北地质大学社会科学部, 河北 石家庄 050031;2.南京信息工程大学数学与统计学院, 江苏 南京 210044 |
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| 基金项目： | 国家自然科学基金资助项目(11871189) |
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| 摘 要： | 研究基于多值逻辑MV-代数的度量型模糊粗糙集模型,给出-半度量和通常的实数值半度量的关系,证明-半度量和 -相似关系的等价性,研究-半度量诱导的模糊粗糙近似算子的性质及其可定义集的性质。
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| 关 键 词： | MV-代数 -半度量 -相似关系 模糊粗糙近似算子 可定义集 |
MV-algebra valued metric-based fuzzy rough sets |
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| XIONG Xing-guo,LU Ling-xia.MV-algebra valued metric-based fuzzy rough sets[J].Journal of Shandong University,2019,54(11):81-89. |
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| Authors: | XIONG Xing-guo LU Ling-xia |
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| Institution: | 1. School of Social Science, Hebei GEO University, Shijiazhuang 050018, Hebei, China;2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China |
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| Abstract: | MV-algebra valued metric-based fuzzy rough set model is defined. The interrelations between -hemimetrics and the standard real valued hemimetrics are investigated. It is shown that -hemimetrics and -similarities are equivalent to each other. The properties of fuzzy rough approximation operators and the related definable sets are studied. |
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| Keywords: | MV-algebra -hemimetric -similarity fuzzy rough approximation operator definable set |
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