模糊數(shù)排序

頁數(shù) 51 字數(shù) 11196

摘 要

本文基于模糊數(shù)的理論，在Yager and Filev所提出的模糊數(shù)權重思想之上，針對模糊數(shù)的排序，提出了一種新的排序的方法，這種方法的提出很好的解決了以前存在的問題。在論文中，分析了公式要處理的六種情況，并且，推導出了運用公式處理這六種情況所產(chǎn)生的結果，這樣以來，就可以在處理排序問題的時候直接運用公式推導出的結果進行討論，簡化了以往討論的復雜性。進一步用圖象來分析公式的幾何意義，運用matlab給出了形變因子對模糊數(shù)的影響的圖像，經(jīng)過圖像分析之后，我們在形變因子對隸屬度函數(shù)影響的方面有個很清晰的認識。最后針對滿意度公式，提出具有代表性的數(shù)值例子進行說明。
在不同的形變因子影響之下，得到排序的結果也不相同。公式的提出很好的處理了結果的單一性，可以根據(jù)對結果所產(chǎn)生的圖像進行分析，得出需要的結果。

關鍵字 模糊數(shù),排序,形變因子

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 錄

中文摘要...........................................................................................................................Ⅰ
英文摘要...........................................................................................................................Ⅱ
1 序言.................................................................................................................................1
1.1 模糊數(shù)課題的引入..............................................................................................1
1.2 研究的基礎以及思想..........................................................................................1
1.3 研究所要達到的效果..........................................................................................1
1.4 本文點題..............................................................................................................2
2 模糊數(shù)理論基礎.............................................................................................................3
3 Yager and Filev提出的排序方法...................................................................................5
3.1 Yager排序方法....................................................................................................5
3.2 形變因子的影響.................................................................................................5
4 公式的提出.....................................................................................................................8
4.1 提出滿意度公式..................................................................................................8
4.2 對滿意度公式分析..............................................................................................9
4.2.1 分析公式遇到的第一種情況...................................................................9
4.2.2 分析運用公式遇到的第二種情況 .........................................................13
4.2.3 分析運用公式遇到的第三、四種情況...................................................19
4.2.4 分析運用公式遇到的第五、六種情況 .................................................22
5 分析公式的幾何意義.....................................................................................................24
6 運用數(shù)值例子圖象說明.................................................................................................26
6.1 圖象說明q對Yager and Filev 提出的數(shù)值的影響..........................................26
6.2 圖象說明q對滿意度影響..................................................................................28
6.2.1 對滿意度的第一個例子...........................................................................28
6.2.2 相對于第一個例子的例子.......................................................................29
7 結束語.............................................................................................................................32
致謝.....................................................................................................................................33
參考文獻.............................................................................................................................34
附錄A：英文原文..............................................................................................................35
附錄B：漢語翻譯..............................................................................................................42
附錄C：matlab代碼..........................................................................................................47

參考文獻

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