本文選題：模糊數(shù) + 高斯型模糊數(shù)　； 參考：《杭州電子科技大學(xué)》2015年碩士論文

【摘要】：1965年,模糊集這一概念第一次被美國控制論專家Zadeh教授在’'Fuzzy Sets"一文中提出。緊接著,在1972年,Chang和Zadeh提出了模糊數(shù)這一概念,并且對模糊數(shù)隸屬函數(shù)的性質(zhì)進(jìn)行了研究。隨著模糊數(shù)理論和應(yīng)用的不斷發(fā)展和完善,使得它變得越來越重要。例如,在2009年,Wang, Shi和Paul提出了不確定多通道數(shù)字信息空間的表示方法,以及討論了基于模糊n-cell數(shù)空間距離和區(qū)別值在模式識別中的應(yīng)用。在2013年,Ramesh和Jena討論了高斯型隸屬函數(shù)的模糊聚類。由于三角形模糊數(shù)和梯形模糊數(shù)結(jié)構(gòu)簡單,易于構(gòu)造,所以在工程應(yīng)用中非常受歡迎。也因其應(yīng)用的需求,關(guān)于它們的理論研究已經(jīng)取得了蓬勃的發(fā)展。然而,總是用線性函數(shù)去表示一個模糊量是不合適的。雖然用它們?nèi)ヌ幚硪恍⿺?shù)據(jù)比較方便快捷,但有時候用它們?nèi)ケ硎疽恍┎淮_定或不精確的數(shù)字信息時,在準(zhǔn)確性方面存在一些缺陷。例如,如果我們用正規(guī)點是172(單位：厘米),支撐集是[166,178](單位：厘米)的三角形模糊數(shù)u去表示在某個地區(qū)男性中等身高的模糊量。則可得到“(171)=0.83,它就意味著一個身高171cm的人屬于中等身高男性的高度的隸屬度是0.83,這個隸屬度和實際相比似乎有點小。本文將討論一種特殊的模糊數(shù)——高斯型模糊數(shù)。它不僅繼承了梯形模糊數(shù)和三角形模糊數(shù)應(yīng)用的方便性,而且能更準(zhǔn)確的表示一些不確定或不精確的數(shù)字信息。本文所做工作具體安排如下：1.在第一部分,主要介紹了有關(guān)研究工作的背景,目的和意義。2.在第二部分,介紹了有關(guān)模糊數(shù)集合理論和模糊數(shù)的一些基本概念。3.在第三部分,(1)給出了高斯型模糊數(shù)的定義,討論了其基本運算性質(zhì)；證明了對于高斯型模糊數(shù),通常的由Zadeh擴(kuò)張原理定義的加法運算已不再保持其運算的封閉性,而由Zadeh擴(kuò)張原理定義的數(shù)乘運算仍保持其運算的封閉性；并給出了由Zadeh擴(kuò)張原理定義的加法運算保持其運算封閉性的條件。(2)為了實際應(yīng)用方便,我們給出了限制在高斯型模糊數(shù)空間的均值和離散度的具體計算公式(在實際應(yīng)用中,易于通過編程實現(xiàn)其計算)。(3)定義了高斯型模糊數(shù)空間上的幾種距離,并討論了幾種距離的特點和性質(zhì),以便在實際應(yīng)用中根據(jù)實際應(yīng)用背景選取較適合的距離來處理問題。(4)討論了高斯型模糊數(shù)空間的幾種序關(guān)系以及每一種序所具有的性質(zhì)。(5)給出了限制在高斯型模糊數(shù)空間的區(qū)別值和近似關(guān)系的具體表式。4.在第四部分,首先,我們討論了對于一組不確定或不精確的數(shù)字信息,如何構(gòu)造高斯型模糊數(shù)來表示這組數(shù)字信息。然后,我們通過例子說明如何對高斯型模糊數(shù)進(jìn)行排序和分類。最后,給出一個實際例子,說明高斯型模糊數(shù)在模式識別中的應(yīng)用。5.在第五部分,我們主要對文章內(nèi)容進(jìn)行了總結(jié),并展望未來的研究工作。
[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.
【學(xué)位授予單位】：杭州電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O159

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