三角模糊数判断矩阵理论及排序方法研究  

Triangular Fuzzy Number Judgment Matrix Theory and Priority Method

作　　者：张慧哲[1] 王坚[1] 任子晖[1] 

机构地区：[1]同济大学CIMS研究中心,上海201804

出　　处：《模糊系统与数学》2009年第4期120-125,共6页Fuzzy Systems and Mathematics

基　　金：国家"863"计划项目(2003AA414120);国家科技支撑计划项目(2006BAF01A46);上海市社会发展重大专项项目(06DZ12001);上海市基础研究重点项目(06JC14066);上海市科技发展基金重点资助项目(061612058);上海市登山行动计划项目(061111006)

摘　　要：由于三角模糊数运算的复杂性和特殊性,许多经典判断矩阵的理论并非完全适用于三角模糊数判断矩阵。首先指出目前文献中三角模糊数判断矩阵排序向量研究中存在的问题,并对经典判断矩阵的理论和性质在三角模糊数中是否完全适用进行了证明,然后基于已经证明在三角模糊数判断矩阵所适用的性质,分别建立了最小二乘法的三角模糊数互反互补判断矩阵目标优化模型,通过求解其模型可得到矩阵的权重向量,最后利用已有的三角模糊数排序公式求得决策结果。算例分析验证了该方法的正确性和有效性。Many classical judgment matrix theories can not be applied to triangular fuzzy judgment matrix owing to its complexity and particularity. Firstly,the problems of triangular fuzzy judgment matrix priority weight in existing papers are proposed, and proved the properties of classical judgment matrix are right when they are applied to triangular fuzzy judgment matrix. Based on the properties proved, least square method programming model of triangular fuzzy reciprocal and complementary judgment matrix are estab- lished. The weight vector of triangular fuzzy judgment matrix is obtained by solving the model. By using an existing priority formula of triangular fuzzy numbers, the decision alternatives are ranked. Finally, a numerical example is given, and result valid the validity and effectiveness of the method in this paper.

关 键 词：三角模糊数 互反判断矩阵 互补判断矩阵 排序 最小二乘法 

分 类 号：TP311[自动化与计算机技术—计算机软件与理论]