| 一类二元函数连续性的等价刻画及在三角模上的应用 |
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| 引用本文： | 张德利,郭彩梅.一类二元函数连续性的等价刻画及在三角模上的应用[J].模糊系统与数学,2007,21(4):6-8. |
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| 作者姓名： | 张德利 郭彩梅 |
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| 作者单位： | 1. 吉林省教育学院,吉林,长春,130022
2. 长春大学,基础科学系,吉林,长春,130022 |
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| 基金项目： | 国家自然科学基金资助项目(10271035) |
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| 摘 要： | 关于二元函数的连续,经典数学分析中有熟知的结果,即"如果二元函数连续,则必关于每个单变量连续。反之,则未必"。本文证明对于单调且对称的二元函数而言,其二元连续等价于单变量连续,并重新定义了三角模的连续。
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| 关 键 词： | 二元函数 连续 三角模 |
| 文章编号： | 1001-7402（2007）04-0006-03 |
| 收稿时间： | 2006-03-13 |
| 修稿时间： | 2006年3月13日 |
An Equivalent Statement on the Continuity of a Class of Two Variables Functions and Its Application on Triangular Norms |
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| ZHANG De-li,GUO Cai-mei.An Equivalent Statement on the Continuity of a Class of Two Variables Functions and Its Application on Triangular Norms[J].Fuzzy Systems and Mathematics,2007,21(4):6-8. |
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| Authors: | ZHANG De-li GUO Cai-mei |
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| Institution: | 1. Jilin Prov. Inst. of Education,Changchun 130022,China;2. Department of Basic Seienee,Changehun University,Changehun 130022,China |
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| Abstract: | As to the continuity of a two variables function,there exists the familiar result in the classical analysis,i.e.A two variables function is continuous on each variable if it is continuous,and the contrary is not correct.The present paper proves that: For a monotone and commutative two variables function, its continuity is equivalent to the continuity on each variable,and the continuity of triangular.Norms is redefined. |
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| Keywords: | Two Variables Function Continuous Triangular Norm |
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