区间粗糙数层次分析法若干问题研究

发布时间：2018-03-23 05:11

本文选题：粗糙集　切入点：层次分析法　出处：《广西大学》2017年硕士论文　论文类型：学位论文

【摘要】：粗糙集理论(RS)主要用于处理不完备信息,优势在于不需任何先验知识,层次分析法(AHP)可用于定性和定量分析,优势在于科学地考虑主观经验,将二者结合应用于决策问题具有重要意义。目前结合方式主要有两种:一是简单组合,本质上未产生新方法;二是粗糙数的方式,但仅考虑属性取值或权重是区间粗糙数,尚未考虑方案间比较判断为区间粗糙数的情形,且未形成完整的基于粗糙集的层次分析理论。论文通过构造区间粗糙数判断矩阵,将RS客观性和AHP主观性有机结合,形成区间粗糙数层次分析法,丰富了 RS与AHP结合的多属性决策方法研究。主要研究内容如下:一是分析现有区间粗糙数大小比较方法,给出一种期望和方差结合的比较方法,以及提出一个带决策者偏好的区间粗糙数优先可能度的定义,并对其性质展开讨论,进而给出基于优先可能度的区间粗糙数排序方法。二是分析现有标度系统和决策者判断的不确定性,考虑判断比值为区间粗糙数,利用云模型中的正逆向云发生器得到区间粗糙标度表示方法。三是通过区间粗糙标度构造区间粗糙数形式的判断矩阵,在不确定中又带有一定的精确性,使得判断值较大概率落入给定的更小区间中,求解排序向量得到最终方案的排序,从而系统地构建区间粗糙数层次分析法。
[Abstract]:Rough set theory is mainly used to deal with incomplete information. Its advantage is that it does not need any prior knowledge, the analytic hierarchy process (AHP) can be used for qualitative and quantitative analysis, and the advantage lies in the scientific consideration of subjective experience. It is very important to apply the two methods to the decision making problem. At present, there are two main ways of combination: one is simple combination, the other is rough number, but only considering attribute value or weight is interval rough number. The case that the comparison between schemes is judged as interval rough number has not been considered, and a complete hierarchical analysis theory based on rough set has not been formed. By constructing interval rough number judgment matrix, RS objectivity and AHP subjectivity are combined organically. An interval rough number analytic hierarchy process is formed, which enriches the study of multi-attribute decision making method combining RS and AHP. The main contents are as follows: firstly, the existing interval rough number comparison methods are analyzed, and a comparison method of combining expectation and variance is given. In addition, a definition of interval rough number priority possibility degree with decision makers' preference is proposed, and its properties are discussed. The second is to analyze the uncertainty of the existing scale system and the decision maker, and consider the ratio of judgment to be interval rough number. Using the positive and reverse cloud generator in the cloud model to obtain the interval rough scale representation method. Third, the interval rough scale is used to construct the judgment matrix of interval rough number form, which has certain accuracy in the uncertainty. The higher probability of the judgment value falls into the given interval, and the ranking vector is solved to get the ranking of the final scheme, and then the interval rough number analytic hierarchy process (AHP) is systematically constructed.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F724.6;F572

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