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題名 Interval-valued and fuzzy-valued random variables: from computing sample variances to computing sample covariances
作者 Beck, Jan B.
Kreinovich, Vladi
吳柏林
Wu, Berlin
貢獻者 應數系
關鍵詞 Interval Arithmetic ; Interval Uncertainty ; Random Interval ; Interval Computation ; Computing Versus
日期 2004
上傳時間 11-Sep-2018 17:58:53 (UTC+8)
摘要 Due to measurement uncertainty, often, instead of the actual values xi of the measured quantities, we only know the intervals xi=[x~i−Δi,x~i+Δi], where x~i is the measured value and Δi is the upper bound on the measurement error (provided, e.g., by the manufacturer of the measuring instrument). These intervals can be viewed as random intervals, i.e., as samples from the interval-valued random variable. In such situations, instead of the exact value of the sample statistics such as the covariance Cxy, we can only have an interval Cx,y of possible values of this statistic. It is known that in general, computing such an interval Cx,y for Cxy is an NP-hard problem. In this paper, we describe an algorithm that computes this range Cx,y for the case when the measurements are accurate enough—so that the intervals corresponding to different measurements do not intersect much.
關聯 Soft methodology and random information systems, 85-92, Adv. Soft Comput., Springer, Berlin, 2004
Part of the Advances in Soft Computing book series (AINSC, volume 26)
資料類型 conference
DOI https://doi.org/10.1007/978-3-540-44465-7_9
dc.contributor 應數系
dc.creator (作者) Beck, Jan B.en_US
dc.creator (作者) Kreinovich, Vladien_US
dc.creator (作者) 吳柏林zh_TW
dc.creator (作者) Wu, Berlinen_US
dc.date (日期) 2004
dc.date.accessioned 11-Sep-2018 17:58:53 (UTC+8)-
dc.date.available 11-Sep-2018 17:58:53 (UTC+8)-
dc.date.issued (上傳時間) 11-Sep-2018 17:58:53 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/120062-
dc.description.abstract (摘要) Due to measurement uncertainty, often, instead of the actual values xi of the measured quantities, we only know the intervals xi=[x~i−Δi,x~i+Δi], where x~i is the measured value and Δi is the upper bound on the measurement error (provided, e.g., by the manufacturer of the measuring instrument). These intervals can be viewed as random intervals, i.e., as samples from the interval-valued random variable. In such situations, instead of the exact value of the sample statistics such as the covariance Cxy, we can only have an interval Cx,y of possible values of this statistic. It is known that in general, computing such an interval Cx,y for Cxy is an NP-hard problem. In this paper, we describe an algorithm that computes this range Cx,y for the case when the measurements are accurate enough—so that the intervals corresponding to different measurements do not intersect much.en_US
dc.format.extent 71147501 bytes-
dc.format.mimetype application/pdf-
dc.relation (關聯) Soft methodology and random information systems, 85-92, Adv. Soft Comput., Springer, Berlin, 2004
dc.relation (關聯) Part of the Advances in Soft Computing book series (AINSC, volume 26)
dc.subject (關鍵詞) Interval Arithmetic ; Interval Uncertainty ; Random Interval ; Interval Computation ; Computing Versusen_US
dc.title (題名) Interval-valued and fuzzy-valued random variables: from computing sample variances to computing sample covariancesen_US
dc.type (資料類型) conference
dc.identifier.doi (DOI) 10.1007/978-3-540-44465-7_9
dc.doi.uri (DOI) https://doi.org/10.1007/978-3-540-44465-7_9