Sequencing of Complementary and Judgment Fuzzy-matrix on the Basis of Structured Element theory

Abstract

Abstract: Use fuzzy structured element method to study the decision-making information to the fuzzy number complementary judgment matrix given in the form of a limited program decision-making problems. The combined-sequence which is more simpler for sorting fuzzy numbers is introduced. In the sequence, and on the basis of the combined-sequence, and some properties of the operator of the FOWA are proved. The operator can reflect preferences-degree of risk of the decision maker's, and the complementary judgment matrix of fuzzy numbers can be turn into real numbers matrix by using the operator, furthermore ,that sequencing complementary and judgment fuzzy——matrix can be turned into sequencing real-number matrix. As long as the element of the matrix is bounded-closed fuzzy numbers, FOWA operator can be used to sort. Finally, a example is given, and it is shown that the method proposed in this paper is more simpler.

Key words: fuzzy complementary judgement matrix, structured element, fuzzy ordered weightedaveraging(FOWA)operator, priority

摘要： 利用模糊结构元方法,研究了决策信息以模糊数互补判断矩阵形式给出的有限方案决策问题。给出了模糊数互补判断矩阵的定义,介绍了模糊数排序的一种简捷方法——组合序。在该序的基础上,对模糊有序加权平均(FOWA)算子的若干性质进行证明。利用该算子能够将模糊数互补判断矩阵转换为实数矩阵,进而,对模糊数互补矩阵的排序问题转换成实数矩阵的排序问题。只要矩阵中的元为有界闭模糊数,就可以利用FOWA算子进行排序。最后通过算例对比分析,算例表明利用本文的方法进行排序更为简捷。

关键词: 模糊数互补判断矩阵, 结构元, 模糊有序加权平均(FOWA)算子, 排序

CLC Number:

F224.32

YUE Li-zhu, MA Wei-min. Sequencing of Complementary and Judgment Fuzzy-matrix on the Basis of Structured Element theory[J]. Operations Research and Management Science, 2013, 22(4): 120-125.

岳立柱, 马卫民. 基于结构元方法的模糊数互补判断矩阵排序法[J]. 运筹与管理, 2013, 22(4): 120-125.

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