| 区间数排序方法综述 |
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| 引用本文： | 李德清,曾文艺,尹乾.区间数排序方法综述[J].北京师范大学学报(自然科学版),2020,56(4):483-492. |
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| 作者姓名： | 李德清 曾文艺 尹乾 |
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| 作者单位： | 1.厦门工学院计算机与人工智能学院， 361021，福建厦门 |
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| 基金项目： | 国家自然科学基金资助项目(61973330，10971243，61472043) |
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| 摘 要： | 区间数排序方法是不确定性决策领域的重要研究内容. 为便于研究者进一步分析和讨论，本文系统总结了目前发表在各类文献中的区间数排序方法，将众多研究者提供的排序方法梳理成9类，分析比较了每一类方法的特点、适用情况，对一些有不足的排序方法通过反例给出了说明. 特别是对目前应用最为广泛的基于可能度的区间数排序方法，讨论了各种不同的可能度公式，指出了它们各自的特点，分析了可能度公式的性质，证明了一些公式相互等价. 同时从可能度和保序性2个角度，分析了基于可能度矩阵的区间数排序方法的不足，并介绍了一种改进的排序方法.
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| 关 键 词： | 区间数 区间数排序 可能度 保序性 |
| 收稿时间： | 2019-06-03 |
Ranking interval numbers: a review |
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| Institution: | 1.School of Computer and Artificial Intelligence，Xiamen Institute of Technology，361021，Xiamen，Fujian，China2.School of Artificial Intelligence，Beijing Normal University，100875，Beijing，China |
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| Abstract: | It is important to rank interval numbers in uncertain decision-making field. Ranking methods of interval numbers are analyzed systematically. Rankings is classified into nine classes. Characteristics and drawbacks of each are discussed. Ranking by possibility degree widely used in uncertain multiple-attribute decision-making is examined in some detail. Different formulas of possibility degree are presented, their features and properties are discussed. Six different possibility formulae are proven equivalent. The popular methodology of ranking a set of interval numbers by possibility degree matrix is investigated. Result obtained by this ranking method is sometimes contrary to the meaning of possibility degree or violates rank preservation. Revised ranking by Boolean matrix is discussed. |
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