發(fā)布時間：2018-11-24 09:27

【摘要】：在對方案或者屬性進(jìn)行兩兩比較的過程中,由于客觀事物的不確定性和復(fù)雜性以及人類對事物認(rèn)識的模糊性和自身知識的局限性,決策者往往給出的是不確定型的判斷矩陣。常見的不確定型判斷矩陣包括區(qū)間型判斷矩陣、直覺判斷矩陣等。關(guān)于這兩類判斷矩陣的研究主要集中在如何判定判斷矩陣的一致性以及利用判斷矩陣的一致性對方案進(jìn)行排序等方面。一方面,本文研究了直覺判斷矩陣的一致性與區(qū)間互補(bǔ)判斷矩陣的一致性以及如何利用這些一致性確定方案的權(quán)重；另一方面,由于個體的差異性,決策者們對方案或者屬性給出的偏好信息類型往往是不同的,例如模糊互補(bǔ)判斷矩陣、區(qū)間互補(bǔ)判斷矩陣、直覺判斷矩陣,因此,本文也研究了區(qū)間互補(bǔ)判斷矩陣、直覺判斷矩陣轉(zhuǎn)化為模糊互補(bǔ)判斷矩陣的方法以及轉(zhuǎn)化過程中的相關(guān)性質(zhì)。本論文的主要研究內(nèi)容如下：(1)研究了基于直覺判斷矩陣有向圖的方案排序方法。根據(jù)直覺模糊數(shù)的特點(diǎn)給出了直覺判斷矩陣有向圖的概念,并指出了直覺判斷矩陣有向圖有惟一有向路的條件。針對具有弱傳遞性的直覺判斷矩陣,本文給出了一種基于直覺判斷矩陣有向圖的方案排序方法。(2)給出了直覺判斷矩陣的加型一致性新定義與確定方案權(quán)重的方法。通過反例說明了直覺判斷矩陣的加型一致性與直覺判斷矩陣的弱傳遞性之間沒有強(qiáng)弱關(guān)系,分析出其傳統(tǒng)加型一致性定義的不足。根據(jù)直覺模糊數(shù)的特性提出了直覺判斷矩陣加型一致性的新定義,并將之應(yīng)用得到確定方案權(quán)重的中轉(zhuǎn)法。另外,從直覺判斷矩陣與權(quán)重之間的關(guān)系角度重新給出了直覺判斷矩陣加型一致性的新定義并利用其確定權(quán)重。(3)研究了區(qū)間互補(bǔ)判斷矩陣的擬一致性。分析了模糊互補(bǔ)判斷矩陣的加型一致性和積型一致性,發(fā)現(xiàn)它們蘊(yùn)含了相對優(yōu)勢度的特點(diǎn),利用這個特點(diǎn)給出了區(qū)間互補(bǔ)判斷矩陣的擬加型一致性、擬積型一致性概念。說明了它們本質(zhì)上是相同的,因此統(tǒng)一地稱之為區(qū)間互補(bǔ)判斷矩陣擬一致性。分別針對擬一致性區(qū)間互補(bǔ)判斷矩陣及一般的區(qū)間互補(bǔ)判斷矩陣,建立了模型求解其區(qū)間數(shù)型權(quán)重。(4)研究了區(qū)間互補(bǔ)判斷矩陣、直覺判斷矩陣轉(zhuǎn)化為模糊互補(bǔ)判斷矩陣中的相關(guān)性質(zhì)。針對模糊互補(bǔ)判斷矩陣、區(qū)間互補(bǔ)判斷矩陣、直覺判斷矩陣給出了如何對這三種偏好關(guān)系進(jìn)行一致化并進(jìn)行集結(jié)的方法。首先分析了模糊互補(bǔ)判斷矩陣的特點(diǎn),利用這個特點(diǎn)將區(qū)間互補(bǔ)判斷矩陣、直覺判斷矩陣均轉(zhuǎn)化為模糊互補(bǔ)判斷矩陣,從而實現(xiàn)了這三類判斷矩陣的一致化。然后研究了轉(zhuǎn)換過程的合理性。
[Abstract]:In the process of comparing schemes or attributes, due to the uncertainty and complexity of objective things, the ambiguity of human cognition and the limitation of their own knowledge, the decision makers often give an uncertain judgment matrix. The common uncertain judgment matrix includes interval judgment matrix, intuitive judgment matrix and so on. The research on these two kinds of judgment matrices is mainly focused on how to judge the consistency of judgment matrices and how to use the consistency of judgment matrices to sort schemes. On the one hand, this paper studies the consistency of intuitionistic judgment matrix and interval complementary judgment matrix, and how to use these consistency to determine the weight of the scheme. On the other hand, due to individual differences, the preference information given by decision-makers to schemes or attributes is often different, such as fuzzy complementary judgment matrix, interval complementary judgment matrix, intuitive judgment matrix. This paper also studies the interval complementary judgment matrix, the method of transforming the intuitionistic judgment matrix into fuzzy complementary judgment matrix and the related properties in the process of transformation. The main contents of this thesis are as follows: (1) the scheme ordering method based on intuitionistic judgement matrix directed graph is studied. According to the characteristics of intuitionistic fuzzy numbers, the concept of directed graph of intuitionistic judgment matrix is given, and the condition that the directed graph of intuitionistic judgment matrix has unique directed path is pointed out. For the intuitionistic judgment matrix with weak transitivity, this paper presents a scheme ordering method based on directed graph of intuitionistic judgment matrix. (2) A new definition of additive consistency of intuitionistic judgment matrix and a method of determining scheme weight are given. It is shown that there is no strong or weak relation between additive consistency of intuitionistic judgment matrix and weak transitivity of intuitionistic judgment matrix by counterexample, and the deficiency of traditional definition of additive consistency is analyzed. According to the characteristics of intuitionistic fuzzy numbers, a new definition of additive consistency of intuitionistic judgment matrix is proposed and applied to the transfer method to determine the weight of the scheme. In addition, a new definition of additive consistency of intuitionistic judgment matrix is redefined from the angle of the relationship between intuitionistic judgment matrix and weight. (3) Quasi-consistency of interval complementary judgment matrix is studied. In this paper, the additive consistency and product consistency of fuzzy complementary judgment matrix are analyzed. It is found that they contain the characteristics of relative advantage degree. By using this characteristic, the concepts of quasi-additive consistency and quasi-product consistency of interval complementary judgment matrix are given. It is shown that they are essentially the same, so they are uniformly called quasi consistency of interval complementary judgment matrix. For the quasi-consistent interval complementary judgment matrix and the general interval complementary judgment matrix, the model is established to calculate the interval number type weights. (4) the interval complementary judgment matrix is studied. The intuitionistic judgment matrix is transformed into the correlation property of fuzzy complementary judgment matrix. Aiming at fuzzy complementary judgment matrix, interval complementary judgment matrix and intuitionistic judgment matrix, this paper gives a method of how to unify and assemble these three preference relations. Firstly, the characteristics of fuzzy complementary judgment matrix are analyzed, and the interval complementary judgment matrix and intuitionistic judgment matrix are transformed into fuzzy complementary judgment matrix by using this characteristic, thus realizing the uniformity of these three kinds of judgment matrices. Then the rationality of the conversion process is studied.
【學(xué)位授予單位】：合肥工業(yè)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：O151.21

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