| 模糊数非单调变换下的结构元表示 |
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| 引用本文： | 岳立柱,仲维清.模糊数非单调变换下的结构元表示[J].模糊系统与数学,2012,26(1):20-24. |
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| 作者姓名： | 岳立柱 仲维清 |
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| 作者单位： | 1. 同济大学经济与管理学院,上海,200092
2. 辽宁工程技术大学继续教育学院,辽宁阜新,123000 |
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| 摘 要： | 在模糊数的结构元表示B~=f(E)中,要求f(x)在-1,1]上单调,将f(x)扩展为-1,1]上的连续函数,在证明f(E)是有界模糊数的基础上,给出了相应模糊数的隶属函数表达形式。由于单调性质在模糊数的运算表示中具有重要作用,还得出非单调连续函数f(x)的E-等价函数概念,并给出了E-等价函数的求法。对于算例,用结构元理论是无法求解的,用本文的方法给出解答。
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| 关 键 词： | 模糊数 结构元 单调 |
The Fuzzy Number Is Expressed by Using the Structured Element When It Is Non-monotonic Transformation |
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| YUE Li-zhu
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ZHONG Wei-qing.The Fuzzy Number Is Expressed by Using the Structured Element When It Is Non-monotonic Transformation[J].Fuzzy Systems and Mathematics,2012,26(1):20-24. |
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| Authors: | YUE Li-zhu ZHONG Wei-qing |
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| Institution: | 1.School of Economic and Management,Tongji University,Shanghai 200092,China;2.Continuing Education School,Liaoning Technical University,Fuxin 123000,China) |
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| Abstract: | When the fuzzy number is expressed by using structured element it is required that f(x) is monotone in ,this will be extended to continuous functions in ,it is proved that f(x) is bounded fuzzy number,on base of it,the membership function of fuzzy number is expressed correspondingly.As the monotonous nature play an important role in the operations of fuzzy numbers,the equivalent function concept of non-monotonic continuous function is concluded in this paper,and how to calculate equivalent function.When the example cannot be solved by using the structured element theory it can be solved by using this method. |
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| Keywords: | Fuzzy Number Structured Element Monotone |
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