Interval Weight Estimation Methods Satisfying Desirable Properties in Interval AHP
Interval Weight Estimation Methods Satisfying Desirable Properties in Interval AHP
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DOI：
10.1007/978-3-030-21920-8_7
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发表时间：
2019-06
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影响因子：
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通讯作者：
M. Inuiguchi
中科院分区：
文献类型：
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作者：
M. Inuiguchi
从两两比较矩阵的不一致性源于决策者评价的模糊性的角度出发，提出用区间权重来表示模糊性的区间层次分析法。事实证明，传统估计方法估计的区间权向量不能很好地反映模糊性。已经提出了几种替代估计方法。然而，这些方法并不总是满足以下期望的性质，而传统方法却满足：（0）该方法是无参数的，（i）给定的成对比较矩阵在估计的区间权重向量下是可实现的，（ii）在一致的清晰成对比较矩阵下估计唯一精确的清晰权向量，（iii）估计的区间权重向量满足正态性条件，以及（iv）从一致的区间成对比较矩阵估计适当的区间权重向量。在本文中，我们证明了以前的替代估计方法不满足其中一些属性，并提出了满足这五个要求的新颖的区间权重估计方法。本文还考虑了最优归一化区间权向量的非唯一性。
From the viewpoint that the inconsistency of a pairwise comparison matrix comes from the vagueness of decision maker’s evaluation, interval AHP representing the vagueness as interval weights was proposed. It has been shown that the interval weight vector estimated by the conventional estimation method does not reflect the vagueness well. Several alternative estimation methods have been proposed. However, those methods do not always satisfy the following desirable properties while the conventional method does: (0) the method is parameter-free, (i) the given pairwise comparison matrix is realizable under the estimated interval weight vector, (ii) the unique accurate crisp weight vector is estimated under a consistent crisp pairwise comparison matrix, (iii) the estimated interval weight vector satisfies the normality condition and (iv) a proper interval weight vector is estimated from a consistent interval pairwise comparison matrix. In this paper, we show that the previous alternative estimation methods do not satisfy some of those properties and propose novel interval weight estimation methods satisfying those five requirements. The non-uniqueness of optimal normalized interval weight vector is also taken care in this paper.