Multiplicative Consistency Test and Modification Approach of Fuzzy Number Complementary Judgment Matrix

Operations Research and Management Science ›› 2013, Vol. 22 ›› Issue (3): 1-7.

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Multiplicative Consistency Test and Modification Approach of Fuzzy Number Complementary Judgment Matrix

ZHAO Xuan, ZHANG Qiang, ZHU Ji-qiao

School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China

Received:2012-03-22 Online:2013-06-25

模糊数互补判断矩阵的乘性一致性检验及改进方法

赵璇, 张强, 朱吉乔

北京理工大学管理与经济学院,北京 100081

作者简介:赵璇(1986-),女,博士研究生,研究方向:模糊决策与对策;张强(1955-),男,教授,博士生导师,研究方向:模糊决策与对策,不确定系统理论及应用;朱吉乔(1986-),男,硕士研究生,研究方向:管理决策理论与方法。
基金资助:
国家自然科学基金和高等学校博士学科点专项科研基金资助(70771010,71071018, 70801064,20111101110036)

Abstract

Abstract: We research on the multiplicative consistency test and modification approach of fuzzy number complementary judgment matrix. It is based on the Q-operator of fuzzy number and Q-operator matrix of fuzzy number complementary judgment matrix introduced in paper[11]. By constructing characteristic matrix with multiplicative consistency and deviation matrix, we establish a measurement index of the multiplicative consistency degree. Meanwhile, the conception of satisfying multiplicative consistency is given by setting threshold. An improved method is proposed for those not satisfying multiplicative consistency. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Key words: management science and engineering, multiplicative consistency, matrix analysis method, fuzzy number complementary judgment matrix

摘要： 针对模糊数互补判断矩阵的乘性一致性检验及改进问题进行研究。在文献[11]引入模糊数的Q-算子和模糊数互补判断矩阵的Q-算子矩阵概念的基础上,通过构造具有乘性一致性的特征矩阵及偏差矩阵,建立了衡量乘性一致性程度的指标值并用设定阈值的方法给出了满意乘性一致性的概念,对于不满足满意乘性一致性的情况提出了改进方法。最后通过一个算例说明了此方法的可行性。

关键词: 管理科学与工程, 乘性一致性, 矩阵分析方法, 模糊数互补判断矩阵

CLC Number:

C934
O223

ZHAO Xuan, ZHANG Qiang, ZHU Ji-qiao. Multiplicative Consistency Test and Modification Approach of Fuzzy Number Complementary Judgment Matrix[J]. Operations Research and Management Science, 2013, 22(3): 1-7.

赵璇, 张强, 朱吉乔. 模糊数互补判断矩阵的乘性一致性检验及改进方法[J]. 运筹与管理, 2013, 22(3): 1-7.

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Multiplicative Consistency Test and Modification Approach of Fuzzy Number Complementary Judgment Matrix

模糊数互补判断矩阵的乘性一致性检验及改进方法

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