基于高斯型模糊数的不确定信息表示与应用

发布时间：2018-04-16 04:07

本文选题：模糊数 + 高斯型模糊数　；参考：《杭州电子科技大学》2015年硕士论文

【摘要】：1965年,模糊集这一概念第一次被美国控制论专家Zadeh教授在’'Fuzzy Sets"一文中提出。紧接着,在1972年,Chang和Zadeh提出了模糊数这一概念,并且对模糊数隶属函数的性质进行了研究。随着模糊数理论和应用的不断发展和完善,使得它变得越来越重要。例如,在2009年,Wang, Shi和Paul提出了不确定多通道数字信息空间的表示方法,以及讨论了基于模糊n-cell数空间距离和区别值在模式识别中的应用。在2013年,Ramesh和Jena讨论了高斯型隶属函数的模糊聚类。由于三角形模糊数和梯形模糊数结构简单,易于构造,所以在工程应用中非常受欢迎。也因其应用的需求,关于它们的理论研究已经取得了蓬勃的发展。然而,总是用线性函数去表示一个模糊量是不合适的。虽然用它们去处理一些数据比较方便快捷,但有时候用它们去表示一些不确定或不精确的数字信息时,在准确性方面存在一些缺陷。例如,如果我们用正规点是172(单位：厘米),支撑集是[166,178](单位：厘米)的三角形模糊数u去表示在某个地区男性中等身高的模糊量。则可得到“(171)=0.83,它就意味着一个身高171cm的人属于中等身高男性的高度的隶属度是0.83,这个隶属度和实际相比似乎有点小。本文将讨论一种特殊的模糊数——高斯型模糊数。它不仅继承了梯形模糊数和三角形模糊数应用的方便性,而且能更准确的表示一些不确定或不精确的数字信息。本文所做工作具体安排如下：1.在第一部分,主要介绍了有关研究工作的背景,目的和意义。2.在第二部分,介绍了有关模糊数集合理论和模糊数的一些基本概念。3.在第三部分,(1)给出了高斯型模糊数的定义,讨论了其基本运算性质；证明了对于高斯型模糊数,通常的由Zadeh扩张原理定义的加法运算已不再保持其运算的封闭性,而由Zadeh扩张原理定义的数乘运算仍保持其运算的封闭性；并给出了由Zadeh扩张原理定义的加法运算保持其运算封闭性的条件。(2)为了实际应用方便,我们给出了限制在高斯型模糊数空间的均值和离散度的具体计算公式(在实际应用中,易于通过编程实现其计算)。(3)定义了高斯型模糊数空间上的几种距离,并讨论了几种距离的特点和性质,以便在实际应用中根据实际应用背景选取较适合的距离来处理问题。(4)讨论了高斯型模糊数空间的几种序关系以及每一种序所具有的性质。(5)给出了限制在高斯型模糊数空间的区别值和近似关系的具体表式。4.在第四部分,首先,我们讨论了对于一组不确定或不精确的数字信息,如何构造高斯型模糊数来表示这组数字信息。然后,我们通过例子说明如何对高斯型模糊数进行排序和分类。最后,给出一个实际例子,说明高斯型模糊数在模式识别中的应用。5.在第五部分,我们主要对文章内容进行了总结,并展望未来的研究工作。
[Abstract]:In 1965, the concept of fuzzy set was first proposed by American cybernetics expert Professor Zadeh in a paper "Fuzzy Sets".Then in 1972, Chang and Zadeh put forward the concept of fuzzy number, and studied the properties of membership function of fuzzy number.With the development and perfection of fuzzy number theory and application, it becomes more and more important.For example, in 2009, Wang, Shi and Paul proposed a representation method of uncertain multi-channel digital information space, and discussed the application of fuzzy n-cell number space distance and difference value in pattern recognition.In 2013, Jena and Ramesh discussed the fuzzy clustering of Gao Si membership function.Triangular fuzzy numbers and trapezoid fuzzy numbers are very popular in engineering applications because of their simple structure and easy construction.Also because of its application demand, the theory research about them has already obtained the vigorous development.However, it is not appropriate to always express a fuzzy quantity with a linear function.Although it is convenient and fast to use them to deal with some data, sometimes there are some defects in accuracy when they are used to express some uncertain or inaccurate digital information.For example, if we use the triangular fuzzy number u of the support set [166178] (unit: cm) to represent the middle height of a man in a given region, the normal point is 172 (in centimeters).It means that a person with a height of 171cm has a height of 0.83 for a man of medium height, which seems to be a little small compared to reality.This paper will discuss a special fuzzy number-Gao Si type fuzzy number.It not only inherits the convenience of the application of trapezoid fuzzy numbers and triangular fuzzy numbers, but also represents some uncertain or inaccurate digital information more accurately.The details of the work in this paper are as follows: 1.In the first part, it mainly introduces the background, purpose and significance of the research work.In the second part, we introduce the theory of fuzzy number set and some basic concepts of fuzzy number.In the third part, the author gives the definition of Gao Si type fuzzy number, discusses its basic operation properties, and proves that the usual addition operation defined by Zadeh extension principle no longer maintains the closeness of its operation.And the number multiplication operation defined by Zadeh extension principle still keeps the closure of its operation, and the condition that the addition operation defined by Zadeh extension principle keeps its operation closed is given, which is convenient for practical application.In this paper, we give the formulas for calculating the mean value and dispersion of Gao Si fuzzy number space (which is easy to be realized by programming in practice) and define several kinds of distances on Gao Si fuzzy number space.The characteristics and properties of several kinds of distances are also discussed.In order to select the suitable distance according to the practical application background to deal with the problem. (4) this paper discusses several kinds of order relations of Gao Si fuzzy number space and the properties of each order.The concrete expression of the difference value and approximate relation of paste number space. 4.In the fourth part, we first discuss how to construct Gao Si type fuzzy number to represent this set of digital information for a group of uncertain or imprecise digital information.Then, we illustrate how to sort and classify Gao Si fuzzy numbers through examples.Finally, an example is given to illustrate the application of Gao Si fuzzy number in pattern recognition.In the fifth part, we summarize the content of the article and look forward to the future research work.
【学位授予单位】：杭州电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O159

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