模糊数排序.doc
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模糊数排序,页数 51 字数 11196摘 要本文基于模糊数的理论，在yager and filev所提出的模糊数权重思想之上，针对模糊数的排序，提出了一种新的排序的方法，这种方法的提出很好的解决了以前存在的问题。在论文中，分析了公式要处理的六种情况，并且，推导出了运用公式处理这六种情况所产生的结果，这样以来，就可以在处...
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模糊数排序
页数 51 字数 11196
摘 要
本文基于模糊数的理论，在Yager and Filev所提出的模糊数权重思想之上，针对模糊数的排序，提出了一种新的排序的方法，这种方法的提出很好的解决了以前存在的问题。在论文中，分析了公式要处理的六种情况，并且，推导出了运用公式处理这六种情况所产生的结果，这样以来，就可以在处理排序问题的时候直接运用公式推导出的结果进行讨论，简化了以往讨论的复杂性。进一步用图象来分析公式的几何意义，运用matlab给出了形变因子对模糊数的影响的图像，经过图像分析之后，我们在形变因子对隶属度函数影响的方面有个很清晰的认识。最后针对满意度公式，提出具有代表性的数值例子进行说明。
在不同的形变因子影响之下，得到排序的结果也不相同。公式的提出很好的处理了结果的单一性，可以根据对结果所产生的图像进行分析，得出需要的结果。
关键字 模糊数,排序,形变因子
ABSTRACT
According to the theories of the fuzzy number, this article is on the basis of the weight coefficient of fuzzy number which is illustrated by Yager and Filev. We put forward a new method on the order of the fuzzy number, with this method we can resolve the problem in the past. In this article six kinds of conditions have been analyzed, and, using the formula we can deduce the consequence of these six conditions. In this case, we can make use of the consequence directly when we deal with the order of fuzzy numbers. It also simplified the complexity of the former discussion. Further more when we use image to analyze the geometry meaning of formula, using MATLAB, we receive the image of fuzzy number in the influence of weight coefficient, through the analytics of the image, we could clearly understand the influence that weight coefficient to the membership function. At last, aim at the degree of satisfaction formula, we put forward a representative example to illumination.
Under the influence of different weight function, the consequence of the orders are also different. In this way we can receive a good processing conclusion, which is not single. According to the analysis of the image, we can get a conclusion for need.
Key word Fuzzy Number; Order; Weight Function
目 录
中文摘要...........................................................................................................................Ⅰ
英文摘要...........................................................................................................................Ⅱ
1 序言.................................................................................................................................1
1.1 模糊数课题的引入..............................................................................................1
1.2 研究的基础以及思想..........................................................................................1
1.3 研究所要达到的效果..........................................................................................1
1.4 本文点题..............................................................................................................2
2 模糊数理论基础.............................................................................................................3
3 Yager and Filev提出的排序方法...................................................................................5
3.1 Yager排序方法....................................................................................................5
3.2 形变因子的影响.................................................................................................5
4 公式的提出.....................................................................................................................8
4.1 提出满意度公式..................................................................................................8
4.2 对满意度公式分析..............................................................................................9
4.2.1 分析公式遇到的第一种情况...................................................................9
4.2.2 分析运用公式遇到的第二种情况 .........................................................13
4.2.3 分析运用公式遇到的第三、四种情况...................................................19
4.2.4 分析运用公式遇到的第五、六种情况 .................................................22
5 分析公式的几何意义.....................................................................................................24
6 运用数值例子图象说明.................................................................................................26
6.1 图象说明q对Yager and Filev 提出的数值的影响..........................................26
6.2 图象说明q对满意度影响..................................................................................28
6.2.1 对满意度的第一个例子...........................................................................28
6.2.2 相对于第一个例子的例子.......................................................................29
7 结束语.............................................................................................................................32
致谢.....................................................................................................................................33
参考文献.............................................................................................................................34
附录A：英文原文..............................................................................................................35
附录B：汉语翻译..............................................................................................................42
附录C：matlab代码..........................................................................................................47
参考文献
[1] 汪诚义.模糊数学引论.第一版.北京工业学院出版社,1988 :1-14页
[2] 张文修.模糊数学基础.第一版.西安交通大学出版社,1985 :2-3页
[3] 杨纶标,高英仪.模糊数学原理及应用.第四版.华南理工大学出版社,1992 :1-8页
[4] 王铭文,金长泽.模糊数学讲义.第一版.东北师范大学出版社,1987 :1-15,131-134页
[5] 楼世博,孙章.模糊数学.第一版.科学出版社,1983 :1-5页
页数 51 字数 11196
摘 要
本文基于模糊数的理论，在Yager and Filev所提出的模糊数权重思想之上，针对模糊数的排序，提出了一种新的排序的方法，这种方法的提出很好的解决了以前存在的问题。在论文中，分析了公式要处理的六种情况，并且，推导出了运用公式处理这六种情况所产生的结果，这样以来，就可以在处理排序问题的时候直接运用公式推导出的结果进行讨论，简化了以往讨论的复杂性。进一步用图象来分析公式的几何意义，运用matlab给出了形变因子对模糊数的影响的图像，经过图像分析之后，我们在形变因子对隶属度函数影响的方面有个很清晰的认识。最后针对满意度公式，提出具有代表性的数值例子进行说明。
在不同的形变因子影响之下，得到排序的结果也不相同。公式的提出很好的处理了结果的单一性，可以根据对结果所产生的图像进行分析，得出需要的结果。
关键字 模糊数,排序,形变因子
ABSTRACT
According to the theories of the fuzzy number, this article is on the basis of the weight coefficient of fuzzy number which is illustrated by Yager and Filev. We put forward a new method on the order of the fuzzy number, with this method we can resolve the problem in the past. In this article six kinds of conditions have been analyzed, and, using the formula we can deduce the consequence of these six conditions. In this case, we can make use of the consequence directly when we deal with the order of fuzzy numbers. It also simplified the complexity of the former discussion. Further more when we use image to analyze the geometry meaning of formula, using MATLAB, we receive the image of fuzzy number in the influence of weight coefficient, through the analytics of the image, we could clearly understand the influence that weight coefficient to the membership function. At last, aim at the degree of satisfaction formula, we put forward a representative example to illumination.
Under the influence of different weight function, the consequence of the orders are also different. In this way we can receive a good processing conclusion, which is not single. According to the analysis of the image, we can get a conclusion for need.
Key word Fuzzy Number; Order; Weight Function
目 录
中文摘要...........................................................................................................................Ⅰ
英文摘要...........................................................................................................................Ⅱ
1 序言.................................................................................................................................1
1.1 模糊数课题的引入..............................................................................................1
1.2 研究的基础以及思想..........................................................................................1
1.3 研究所要达到的效果..........................................................................................1
1.4 本文点题..............................................................................................................2
2 模糊数理论基础.............................................................................................................3
3 Yager and Filev提出的排序方法...................................................................................5
3.1 Yager排序方法....................................................................................................5
3.2 形变因子的影响.................................................................................................5
4 公式的提出.....................................................................................................................8
4.1 提出满意度公式..................................................................................................8
4.2 对满意度公式分析..............................................................................................9
4.2.1 分析公式遇到的第一种情况...................................................................9
4.2.2 分析运用公式遇到的第二种情况 .........................................................13
4.2.3 分析运用公式遇到的第三、四种情况...................................................19
4.2.4 分析运用公式遇到的第五、六种情况 .................................................22
5 分析公式的几何意义.....................................................................................................24
6 运用数值例子图象说明.................................................................................................26
6.1 图象说明q对Yager and Filev 提出的数值的影响..........................................26
6.2 图象说明q对满意度影响..................................................................................28
6.2.1 对满意度的第一个例子...........................................................................28
6.2.2 相对于第一个例子的例子.......................................................................29
7 结束语.............................................................................................................................32
致谢.....................................................................................................................................33
参考文献.............................................................................................................................34
附录A：英文原文..............................................................................................................35
附录B：汉语翻译..............................................................................................................42
附录C：matlab代码..........................................................................................................47
参考文献
[1] 汪诚义.模糊数学引论.第一版.北京工业学院出版社,1988 :1-14页
[2] 张文修.模糊数学基础.第一版.西安交通大学出版社,1985 :2-3页
[3] 杨纶标,高英仪.模糊数学原理及应用.第四版.华南理工大学出版社,1992 :1-8页
[4] 王铭文,金长泽.模糊数学讲义.第一版.东北师范大学出版社,1987 :1-15,131-134页
[5] 楼世博,孙章.模糊数学.第一版.科学出版社,1983 :1-5页
