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A two-stage logarithmic goal programming method for generating weights from interval comparison matrices

机译：从区间比较矩阵生成权重的两步对数目标规划方法

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摘要

A two-stage logarithmic goal programming (TLGP) method is proposed to generate weights from interval comparison matrices, which can be either consistent or inconsistent. The first stage is devised to minimize the inconsistency of interval comparison matrices and the second stage is developed to generate priorities under the condition of minimal inconsistency. The weights are assumed to be multiplicative rather than additive. In the case of hierarchical structures, a nonlinear programming method is used to aggregate local interval weights into global interval weights. A simple yet practical preference ranking method is investigated to compare the interval weights of criteria or rank alternatives in a multiplicative aggregation process. The proposed TLGP is also applicable to fuzzy comparison matrices when they are transformed into interval comparison matrices using α-level sets and the extension principle. Six numerical examples including a group decision analysis problem with a group of comparison matrices, a hierarchical decision problem and a fuzzy decision problem using fuzzy comparison matrix are examined to show the applications of the proposed methods. Comparisons with other existing procedures are made whenever possible.
机译：提出了一种两阶段对数目标规划（TLGP）方法来从区间比较矩阵生成权重，该权重可以是一致的或不一致的。设计第一阶段以最小化间隔比较矩阵的不一致，而第二阶段被开发为在最小不一致的条件下生成优先级。假定权重是乘法的，而不是加法的。在分层结构的情况下，使用非线性编程方法将局部区间权重聚合为全局区间权重。研究了一种简单而实用的偏好排序方法，以比较乘法聚合过程中标准的间隔权重或对替代项进行排序。当使用α级集和扩展原理将模糊变换矩阵转换为区间比较矩阵时，所提出的TLGP也适用于模糊比较矩阵。检验了六个数值示例，包括带有一组比较矩阵的组决策分析问题，分层决策问题和使用模糊比较矩阵的模糊决策问题，以说明所提出方法的应用。尽可能与其他现有程序进行比较。

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