The median of a random fuzzy number. The 1-norm distance approach

详细信息	查看全文 | 推荐本文 |

• 作者：Beatriz Sinova^a ; ^{sinovabeatriz@uniovi.es} ; Marí ; a Á ; ngeles Gil^a ; Ana Colubi^a ; Stefan Van Aelst^b
• 关键词：1-Norm distance ; Fuzzy arithmetic ; Fuzzy numbers ; Median ; Random fuzzy numbers ; Statistical robustness
• 刊名：Fuzzy Sets and Systems
• 出版年：2012
• 期刊代码：55_01650114
• 类别：cp
• 出版时间：1 August, 2012
• 卷：200
• 期：Complete
• 页码：99-115
• 文件大小：521 K

摘要

In quantifying the central tendency of the distribution of a random fuzzy number (or fuzzy random variable in Puri and Ralescu's sense), the most usual measure is the Aumann-type mean, which extends the mean of a real-valued random variable and preserves its main properties and behavior. Although such a behavior has very valuable and convenient implications, 鈥榚xtreme鈥?values or changes of data entail too much influence on the Aumann-type mean of a random fuzzy number. This strong influence motivates the search for a more robust central tendency measure. In this respect, this paper aims to explore the extension of the median to random fuzzy numbers. This extension is based on the 1-norm distance and its adequacy will be shown by analyzing its properties and comparing its robustness with that of the mean both theoretically and empirically.