| DFI代数的距离函数及其性质 |
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| 引用本文： | 刘慧敏,吴洪博.DFI代数的距离函数及其性质[J].吉林大学学报(理学版),2016,54(2):207-214. |
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| 作者姓名： | 刘慧敏 吴洪博 |
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| 作者单位： | 陕西师范大学 数学与信息科学学院, 西安 710119 |
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| 摘 要： | 考虑分配的Fuzzy蕴涵代数（DFI代数）. 首先将距离函数的概念引入到DFI代数中, 得到了DFI代数中距离函数的一些基本性质, 并给出了在某些特殊的DFI代数(如全序DFI代数)上距离函数的特殊性质； 其次, 在DFI代数中引入一个新运算, 得到了DFI代数距离函数的等价定义和性质; 最后, 根据所引进的距离函数建立相应的距离空间, 并给出了一些性质.
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| 关 键 词： | FI代数 正则FI代数 DFI代数 距离函数 |
| 收稿时间： | 2015-06-15 |
Distance Function of DFI Algebras and Its Properties |
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| LIU Huimin,WU Hongbo.Distance Function of DFI Algebras and Its Properties[J].Journal of Jilin University: Sci Ed,2016,54(2):207-214. |
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| Authors: | LIU Huimin WU Hongbo |
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| Institution: | School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China |
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| Abstract: | In order to further study DFI algebra, firstly, the definition of a distance function in DFI algebra was given. Its properties were discussed, and some special properties of the distance function of some kinds of special DFI algebras, for example, linear DFI algebras were given. Secondly, anew operation was introduced in DFI algebra, and the equivalent definition of the distance function of DFI algebras and some farther properties were given; finally, the corresponding metric space based on the distance function was introduced. |
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| Keywords: | FI algebra regular FI algebra DFI algebra distance function |
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