【作者】 刘芳；

【导师】 兰继斌；

【作者基本信息】 广西大学 ， 运筹学与控制论， 2008， 硕士

【摘要】 多属性决策(或者称之为有限个方案的多目标决策)是现代决策科学的一个重要组成部分,其实质是利用已有的决策信息通过一定的方式对一组(有限个)备选方案进行排序并择优。由于客观世界的复杂性、不确定性以及人类思维的模糊性,在实际决策过程中,决策信息往往以不确定的形式给出,如:区间数,三角模糊数,梯形模糊数,LR模糊数等等,从而不确定性多属性决策理论、方法及应用是目前众多决策研究工作者关注的热点。本文对区间数多属性决策的一些问题进行了分析和研究,主要包括以下几个方面:(1)研究了区间数大小比较的可能度公式,指出了一类区间数可能度公式的不足,根据二维空间的面积提出了新的可能度公式,给出了简单而实用的计算公式并证明其相关的性质,通过实例说明此方法的可行性。(2)针对一致性区间数互补判断矩阵的一致性条件,重新定义了一致性区间数互补判断矩阵和研究其优良性质,并给出了其构造法和根据优先程度的排序方法。(3)考虑了基于一致性区间数互反判断矩阵的多属性决策方法及应用,对于一类一致性区间数互反判断矩阵,给出了一致性区间数互反判断矩阵的新定义,研究了其优良的性质,讨论了其构造法。(4)研究了基于凸组合法的区间数互补判断矩阵的权重问题,根据凸组合原理把区间数互补判断矩阵转化为一族实模糊互补判断矩阵,再将这族矩阵的权重集成作为区间数互补判断矩阵的权重,为了使得这族矩阵的每一权重向量可靠,给出了这族互补判断矩阵的一致性和弱传递性的充要条件,通过实例说明了方法的实用性和有效性。(5)根据决策者的偏好程度,研究了区间数互反判断矩阵的权重问题,把区间数互反判断矩阵转化为实模糊互补判断矩阵,从而由实模糊互补判断矩阵确定方案的排序和择优。更多还原

【Abstract】 Multi-attribute decision making (MADM) is very important in modern decision making analysis, and its main task is, based on the gathered information, how to determine the priority vector of the alternatives. Because of the complexity and uncertainty involved in real-world decision problems and the inherent subjective nature of human judgment, during practical decision process, decision information is sometimes expressed as interval number, triangular fuzzy number, trapezoidal fuzzy number and L-R fuzzy number, and so on. Furthermore, some studies on theories, methods and application of uncertain multi-attribute decision making have attracted much attention. In this thesis, some problems of interval number multi-attribute decision making have been investigated.Firstly, the possibility degree of interval number is studied. After pointing out the imperfection of a sort of possibility degree formula of interval number, a new definition of relative superiority degree describling big or small interval numbers is given from the viewpoint of two-dimensional area, and its properties are proven. Some simple and practical formulas for calculation are presented. A numerical example is computed to explain its feasibility and practicability.Secondly, we analyze a consistent interval number complementary judgment matrix (CINCJM). A new definition of CINCJM is given and its superior properties are investigated. A construction of CINCJM and a method of ranking of alternatives are also presented.Thirdly, a consistent interval number reciprocal judgment matrix (CINRJM) of interval number multi-attribute decision making is considered. A new definition of CINRJM as well as its superior properties are given, and a construction of CINRJM is proposed.Fourthly, the weights of interval number complementary judgment matrix generated in the analytic hierarchy process are investigated. By using convex combination, a family of real complementary judgment matrices are constructed from an interval number complementary judgment matrix. The aggregation of the weights of the family of real complementary judgment matrices is considered as the weight of interval number complementary judgment matrix. In order to make any weight vector of the family of real complementary judgment matrices reliable, the sufficient and necessary conditions of their consistency and weak transitivity are given. A numerical example is also presented to illustrate the validity and practicality of the developed methods.Finally, based on preference relation of decision maker, we illustrate the method and application of interval number multi-attribute decision making. By translating an interval number reciprocal judgment matrix (INRJM) into a real complementary judgment matrix, the weight vector of the INRJM is obtained to rank the alternatives and choose the best.更多还原