摘要
首先通过分析乘性一致模糊互补判断矩阵的定义,给出了衡量判断矩阵一致性程度的新指标,在此基础上,结合区间数互补判断矩阵一致性和满意一致性定义,建立了判断矩阵完全一致和满意一致两种情况下的二次规划模型,通过求解得出判断矩阵的区间权重向量,最后提出了一种新的可能度公式对方案进行排序和择优。通过算例说明了此方法的可行性和简洁性。
First, a simple pragmatic consistency index is developed to check the degree of the consistency of an interval complementary judgment matrix by analyzing the multiplicative consistent fuzzy complementary judgment matrix corresponding to interval complementary judgment matrix. Then two quadratic programming models are proposed to derive the weights for the interval complementary judgment matrix with perfect consistency or satisfactory consistency by analyzing the definitions of perfect consistency and satisfying consistency of interval judgment matrix. Finally a new possibility degree formula is given to rank the interval weights achieved by the two models mentioned above, and choose the best alternative. Two examples are provided to illustrate the validity and practicality of the proposed methods.
出处
《模糊系统与数学》
CSCD
北大核心
2013年第1期124-130,共7页
Fuzzy Systems and Mathematics
基金
广西教育厅科研项目(201106LX248)
广西自然科学基金资助项目(2010GXNSFA013121)
关键词
区间层次分析法
乘性一致
可能度
二次规划
区间数互补判断矩阵
Interval Analytic Hierarchy Process
Multiplicative Consistency
Possibility Degree~ QuadraticProgramming
Interval Complementary Judgment Matrix
