论文标题:模糊数的排序及应用
A Method for Ranking Fuzzy Numbers and Its Application
论文作者
论文导师 裴峥,论文学位 硕士,论文专业 计算机软件与理论
论文单位 西华大学,点击次数 148,论文页数 54页File Size1842K
2008-04-01论文网 http://www.lw23.com/lunwen_354094082/
Interval numbers;; Fuzzy numbers;; Rank;; the Game Theory;; Game with Fuzzy Profit
模糊性是事物客观存在的一种属性。随着模糊集理论的发展,要求排序的领域也越来越广泛,专门讨论排序的文章也越来越多[43]。近些年来人们已提出了近40种有关模糊数的排序方法,这些方法大体上可以分为三类,第一类是将待排序的每个模糊量转化为实数,从而利用实数的自然序关系导出模糊量的序关系;第二类是先通过所有的模糊量构造一个参考集,然后将每个模糊量与该参考集进行比较,进而确定模糊量之间的序关系;第三类是构造模糊量上的模糊关系,通过该模糊关系实现模糊量间的两两比较[42]。这三类方法均是通过构造并处理排序指标来确定模糊量的序关系的,其实质是将模糊量转化为数来讨论的,但由于至今为止尚无一个大家所公认的好的排序方法,有人在拓广排序的应用领域,还有人将神经网络方法用于比较模糊数时准则的学习过程,从而选取符合决策者要求的个性化排序方法。本篇论文的前半部分给出了一种新的模糊数的排序方法。该方法属于第一类。我们将会看到它具有很多较好的性质。 鉴于区间数和夹在两坐标轴之间的线段的特定的对应关系,通过原点到线段的距离,可以给出区间数上的一种测度,利用该测度可对区间数进行排序。借助模糊集的α-水平截集,可以将区间数上的测度推广到模糊数上,成为模糊数上的测度,基于该测度可对模糊数进行排序。之后,我们又分别讨论了有关区间数和模糊数的相关性质。所给出的性质和后面的实例分析说明该方法较符合人们对模糊数的直觉认识。在实例分析中我们将本文所给出的排序方法同其它一些排序方法进行了比较。基于多属性决策问题(MADM)是处理最佳选择的各种属性的,它在现代决策中占有重要的地位,它已被广泛地应用于社会、经济管理、环境、教学、复杂系统等的评价、决策中。由于决策问题中的数据结构在很多情况下是不精确的,所以模糊集理论已被广泛地应用到这类模型中[43]。所以在这篇论文中我们将利用本文所给的排序方法解决一些相关的博弈论中的问题。
The indistinct properties is a kind of attribute which the matter exists.With the development of the fuzzy theory ,there are more and more domains which need to be ranked and there are more and more papers on the ranking fuzzy numbers[43]. There have been about 40 kinds of ranking methods proposed in recent years.These methods can be divided into three classes.The first is transform the fuzzy numbers into the real numbers.The second is setting a comparing set at first,then comparing them with the comparing set and determining a ranking relation.The third is setting a fuzzy relation between the fuzzy numbers and comparing them by the fuzzy relation.The three kinds of methods are all determining the relation by setting and dealing with the fuzzy index [42] .However ,because there has not a good method admitted by people by now,someone is still to propose some new methods. In the first half of this paper, a new method for ranking fuzzy numbers is proposed. Based on decomposition theorem of fuzzy set, firstly, the method considers interval numbers, the relation between lines and interval numbers is discussed in Cartesian coordinates, the distance of dot A to lines 1 is used as evaluation of interval number. Then, integral of all distances is used as evaluation of fuzzy number. Finally, ranking fuzzy numbers is implemented by the evaluations of fuzzy numbers. In order to illustrate the ranking method, numeric example is shown, and for the comparative study, our method is compared with four existing ranking methods. As an example of potential applications, the proposed method is applied to game with Fuzzy Profit.
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