Eliciting dual interval probabilities from interval comparison matrices
Eliciting dual interval probabilities from interval comparison matrices
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DOI：
10.1016/j.ins.2011.12.014
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发表时间：
2012-05
期刊：
影响因子：
--
通讯作者：
P. Guo;Yuanbin Wang
中科院分区：
文献类型：
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作者：
P. Guo;Yuanbin Wang
近年来，利用区间概率处理不确定性问题，如组合、边缘化、条件、贝叶斯推理等得到了广泛的关注。然而，如何从主观判断中得到区间概率仍然是区间概率应用中的一个基本问题。在本文中，区间值成对比较的事件被用来描述一个人的判断，其中一个是更有可能发生在每对事件。从区间比较矩阵出发，利用线性规划问题得到了对偶区间概率。估计的区间概率的比率用于从它们的外部和内部近似区间比较值。换句话说，区间比较值与所获得的区间概率的比率之间的包含关系成立。通过一个新产品开发的算例，说明了如何估计对偶区间概率，并利用区间概率进行决策。
In recent years, dealing with uncertainty using interval probabilities, such as combination, marginalization, condition, Bayesian inferences, has received considerable attention. However, how to elicit interval probabilities from subjective judgment is still a fundamental problem in applications of interval probabilities. In this paper, interval-valued pairwise comparisons of events are used to characterize the judgment of a person about which one is more likely to occur between each pair of events. From the interval comparison matrix, we elicit the dual interval probabilities by linear programming problems. The ratios of the estimated interval probabilities are used to approximate the interval comparison values from the outside and the inside of them. In other words, the inclusion relations between the interval comparison values and the ratios of the obtained interval probabilities hold. A numerical example concerning a new product development is presented to illustrate how to estimate dual interval probabilities and use interval probabilities to make a decision.