本文關(guān)鍵詞： Vague集(值) 相似性度量 區(qū)分度 TOPSIS法 動(dòng)態(tài)信息集結(jié)法　出處：《西安科技大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：近年來,Vague集的相似性度量方法以及基于Vague集的多屬性決策方法的研究受到了國內(nèi)外學(xué)者的高度關(guān)注。1993年,Gau和Buehrer提出了處理模糊信息的理論—Vague集理論,該理論本質(zhì)是對Fuzzy集理論的擴(kuò)展。本文依據(jù)已有的幾種Vague集的相似性度量方法的思想并考慮到棄權(quán)部分對Vague集相似性度量的影響,通過對改進(jìn)的相似性度量方法的證明和實(shí)驗(yàn)數(shù)據(jù)的分析,探討了改進(jìn)后的相似性度量方法對數(shù)據(jù)區(qū)分的影響,在此基礎(chǔ)上將改進(jìn)的相似性度量方法應(yīng)用到多屬性決策之中,通過具體的實(shí)例分析給出了合理的決策結(jié)果。主要內(nèi)容如下:首先,介紹了Vague集的相似性度量的相關(guān)理論,即Vague集的相似性度量的定義、運(yùn)算以及性質(zhì)等,分析了構(gòu)造Vague集的相似性度量方法需滿足的條件、定理。在此基礎(chǔ)上分析了已有的幾種Vague集的相似性度量方法,針對已有相似性度量方法未考慮到棄權(quán)部分對Vague集相似性度量的影響以及對數(shù)據(jù)不能進(jìn)行有效區(qū)分的缺點(diǎn),提出了改進(jìn)的相似性度量方法以及改進(jìn)的加權(quán)相似性度量方法。對改進(jìn)的相似性度量方法的定義的完備性在理論上進(jìn)行了證明,并通過九組隨機(jī)實(shí)驗(yàn)數(shù)據(jù)分析改進(jìn)的相似性度量方法對數(shù)據(jù)的影響,為了進(jìn)一步擴(kuò)大數(shù)據(jù)的范圍,分別在區(qū)間[0,1]上找到以0.1為步長的36*36組數(shù)據(jù)和以步長為0.01的2602*2602組數(shù)據(jù)對幾種度量方法進(jìn)行了分析、比較,可得出改進(jìn)的相似性度量方法對數(shù)據(jù)的區(qū)分度更有效、更高。其次,由于多屬性決策問題存在不確定性,將Vague集理論與多屬性決策的問題相結(jié)合,使得多屬性決策問題的解決更加快捷、有效。通過對基于Vague集理論的多屬性決策算法步驟的分析,針對備選方案的排序是直接影響決策結(jié)果的重要因素,為了能對備選方案進(jìn)行合理的區(qū)分,本文選取了改進(jìn)的Vague集的相似性度量公式作為多屬性決策問題的記分函數(shù)。最后,通過改進(jìn)的Vague集的相似性度量方法在簡單加權(quán)法、TOPSIS法和動(dòng)態(tài)信息集結(jié)方法上的應(yīng)用,即對具體的實(shí)例進(jìn)行分析,并給出了合理的決策結(jié)果。
[Abstract]:In recent years, the research on similarity measurement of vague sets and multi-attribute decision making based on Vague sets has been highly concerned by scholars at home and abroad. In 1993. Gau and Buehrer put forward the theory of dealing with fuzzy information-vague set theory. The essence of this theory is to extend the Fuzzy set theory. According to the idea of several existing similarity measurement methods of Vague sets and considering the influence of waiver part on the similarity measurement of Vague sets. Through the proof of the improved similarity measurement method and the analysis of the experimental data, the influence of the improved similarity measurement method on the data differentiation is discussed. On this basis, the improved similarity measurement method is applied to multi-attribute decision making, and a reasonable decision result is given through concrete examples. The main contents are as follows: first. This paper introduces the theory of similarity measurement of Vague sets, that is, the definition, operation and properties of similarity measurement of Vague sets. The conditions and theorems needed to be satisfied in constructing the similarity measurement methods of Vague sets are analyzed. On this basis, several existing similarity measurement methods of Vague sets are analyzed. The existing similarity measurement methods do not take into account the impact of waiver on similarity measurement of Vague sets and the disadvantage that data can not be effectively distinguished. An improved similarity measurement method and an improved weighted similarity measurement method are proposed. The completeness of the definition of the improved similarity measurement method is proved theoretically. The influence of the improved similarity measurement method on the data is analyzed through nine groups of random experimental data. In order to further expand the range of the data, [In this paper, 36 groups of data with 0.1 step size and 2602 groups of data with step size 0.01 were found to analyze and compare several measurement methods. It can be concluded that the improved similarity measurement method is more effective and higher in data differentiation. Secondly, because of the uncertainty of multi-attribute decision making problem, the Vague set theory is combined with the multi-attribute decision making problem. The solution of multi-attribute decision making problem is faster and more effective. Through the analysis of the steps of multi-attribute decision making algorithm based on Vague set theory. The ranking of alternatives is an important factor that directly affects the decision results, in order to make a reasonable distinction between the alternatives. In this paper, the improved Vague set similarity measurement formula is selected as the score function of the multi-attribute decision making problem. Finally, the simple weighting method is used to measure the similarity of the improved Vague set. The application of TOPSIS method and dynamic information aggregation method is the analysis of concrete examples and the reasonable decision results are given.
【學(xué)位授予單位】：西安科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O159

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