摘要
研究三角模糊数互补判断矩阵的加性一致性及排序问题。从加性一致性角度,讨论了三角模糊数互补判断矩阵与三角模糊数互反判断矩阵之间的相互转化关系,建立了一个基于最小方差的多层次非线性规划模型。通过求解该模型得到三角模糊数互补判断矩阵的权重向量,并利用三角模糊数期望值公式对决策方案的权重向量进行排序。最后通过算例验证该方法的可行性和有效性。
The additive consistency and prioritization methods of triangular fuzzy number complementary judgment matrix are studied. According to the concept of additive consistency, transformation relation between triangular fuzzy number complementary judgment matrix and triangular fuzzy number reciprocal judgment matrix is discussed. A multi-tier non-linear programming model based on least square method is established. The weight vector of the judgment matrix is obtained by solving the model. By using an expected value formula of triangular fuzzy number, the decision alternatives are ranked. Finally, a numerical example is given to test the feasibility and validity of this method.
出处
《系统工程》
CSCD
北大核心
2009年第3期89-92,共4页
Systems Engineering
基金
国家自然科学基金资助项目(60572170)
关键词
三角模糊数互补判断矩阵
加性一致性
排序
多层次非线性规划模型
Triangular Fuzzy Number Complementary Judgment Matrix
Additive Consistency
Prioritization
Multi-tier Non-linear Programming Model
