| 模糊数学中的非标准扩大模型 |
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| 引用本文： | 马春晖,史艳维.模糊数学中的非标准扩大模型[J].浙江大学学报(理学版),2011,38(6):611-613. |
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| 作者姓名： | 马春晖 史艳维 |
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| 作者单位： | 西安建筑科技大学理学院;西安培华学院基础部; |
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| 基金项目： | 陕西省自然科学基金资助项目(2007A12); 陕西省教育厅专项科研项目(JK0507); 西安培华学院校级课题资助项目(PHKT029201011) |
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| 摘 要： | 给出了非标准分析理论中非标准扩大模型在模糊数学中的表现形式及一些性质.首先,对模糊集合进行了非标准扩张,定义了相应的* 模糊集.其次,对模糊集合间的运算也进行了非标准扩张,定义了* 模糊集间的运算,这些运算与一般模糊集间的运算是类似的.最后,借助扩张后的* 模糊集和上、下确界运算,给出了非标准扩大模型在模糊数学中的表现形式,并且从多种角度给出了一些非标准扩大模型的性质.
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| 关 键 词： | style="font-family: 宋体 font-size: 10.5pt mso-bidi-font-family: 宋体 mso-ansi-language: EN-US mso-fareast-language: ZH-CN mso-bidi-language: 共点关系AR-SA">共点关系 " target="_blank">lang="EN-US"> 非标准扩大模型 " target="_blank">lang="EN-US"> *-模糊集 " target="_blank">lang="EN-US"> 单子 |
The nonstandard enlargement in fuzzy mathematics |
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| MA Chun-hui,SHI Yan-wei.The nonstandard enlargement in fuzzy mathematics[J].Journal of Zhejiang University(Sciences Edition),2011,38(6):611-613. |
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| Authors: | MA Chun-hui SHI Yan-wei |
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| Institution: | MA Chun-hui1,SHI Yan-wei2 (1.School of Science,Xi'an University of Architecture and Technology,Xi'an 710055,China,2.Department of Basic Courses,Xi'an Peihua University,Xi'an 710125,China) |
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| Abstract: | The representation of nonstandard enlarged model was shown in fuzzy mathematics,and some properties were obtained.Firstly,the *-fuzzy sets were defined by extending the corresponding fuzzy sets in nonstandard enlargement.Secondly,some operations on fuzzy sets were extended to *-fuzzy sets.Finally,with the *-fuzzy sets and extended operations,the representation and some properties of nonstandard enlargement were obtained in many ways. |
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| Keywords: | concurrent nonstandard enlargement *-fuzzy sets monads |
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