使用启发式等级估计方法的成对比较方法中解的存在性的注记
Notes on the existence of solutions in the pairwise comparisons method using the Heuristic Rating Estimation approach
摘要：
成对比较是一种众所周知的方法，用于对决策者的主观偏好进行建模。该方法的一个流行的实现是基于解决M -成对比较矩阵的特征值问题。这并没有考虑到偏好的实际值。启发式评级估计（HRE）的方法是这种方法的修改，允许建模的参考值。确定偏好的相对顺序是求解由矩阵A和常数项向量b（两者都从M导出）定义的某个线性方程组。文章探讨了这些方程组的性质。特别地，证明了对于某些小的数据不一致，A矩阵是M矩阵，因此HRE方法提出的方程具有唯一的严格正解。
英文摘要：
Pairwise comparisons are a well-known method for modelling of the subjective preferences of a decision maker. A popular implementation of the method is based on solving an eigenvalue problem for M - the matrix of pairwise comparisons. This does not take into account the actual values of preference. The Heuristic Rating Estimation (HRE) approach is a modification of this method in which allows modelling of the reference values. To determine the relative order of preferences is to solve a certain linear equation system defined by the matrix A and the constant term vector b (both derived from M). The article explores the properties of these equation systems. In particular, it is proven that for some small data inconsistency the A matrix is an M-matrix, hence the equation proposed by the HRE approach has a unique strictly positive solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
