模糊数互补判断矩阵的加性一致性

研究带有模糊数的互补判断矩阵的一致性.首先给出三角模糊数、梯形模糊数和混合互补判断矩阵定义,然后引入模糊数的心、心算子以及心矩阵,进而基于心矩阵给出模糊数互补判断矩阵的一致性定义,同时建立可达矩阵给出模糊数互补判断矩阵的一致性判别方法;通过构造和分析偏差矩阵,给出非一致性模糊数互补判断矩阵的加性一致性改进方法.调整时,调整量可以是精确数也可以是模糊数.为了说明方法的可行性,给出了一个算例.该方法的提出,为模糊数互补判断矩阵一致性的判断和改进提供了一个实用方法.

Additive Consistency of Complementary Judgment Matrices with Fuzzy Numbers

The consistency of complementary judgment matrices with fuzzy numbers is studied. Definitions of triangular fuzzy number complementary judgment matrix, trapezoidal fuzzy number complementary judgment matrix as well as hybrid number complementary judgment matrix are given, followed by definitions of core operator and core matrix. Meanwhile, definition of consistency of fuzzy number complementary judgment matrix is given based on core matrix. Method for identifying the degree of additive consistency is given by establishing the reachable matrix. By constructing and analyzing the deviation matrix, approaches to improving the additive consistency of inconsistent triangular fuzzy number complementary judgment matrix, inconsistent trapezoidal fuzzy number complementary judgment matrix and inconsistent hybrid number complementary judgment matrix are proposed. For an inconsistent judgment matrix with fuzzy numbers, the rectifying value can be a fuzzy number or an exact one. A numerical example is given to illustrate the method's practicability. The method proposed provides a feasible approach to judge and improve the consistency of complementary judgment matrix with fuzzy numbers.