Taking into Account Interval (and Fuzzy) Uncertainty Can Lead to More Adequate Statistical Estimates

Ligang Sun; Hani Dbouk; Ingo Neumann; Steffen Schön; Vladik Kreinovich

doi:10.1007/978-3-319-67137-6_41

Taking into Account Interval (and Fuzzy) Uncertainty Can Lead to More Adequate Statistical Estimates

Ligang Sun^*, Hani Dbouk, Ingo Neumann, Steffen Schön, Vladik Kreinovich

^*Corresponding author for this work

University of Texas at El Paso

Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review

Abstract

Traditional statistical data processing techniques (such as Least Squares) assume that we know the probability distributions of measurement errors. Often, we do not have full information about these distributions. In some cases, all we know is the bound of the measurement error; in such cases, we can use known interval data processing techniques. Sometimes, this bound is fuzzy; in such cases, we can use known fuzzy data processing techniques. However, in many practical situations, we know the probability distribution of the random component of the measurement error and we know the upper bound on the measurement error’s systematic component. For such situations, no general data processing technique is currently known. In this paper, we describe general data processing techniques for such situations, and we show that taking into account interval and fuzzy uncertainty can lead to more adequate statistical estimates.

Original language	English
Title of host publication	Fuzzy Logic in Intelligent System Design
Subtitle of host publication	theory and applications
Publisher	Springer Verlag
Pages	371-381
Number of pages	11
ISBN (Electronic)	978-3-319-67137-6
ISBN (Print)	978-3-319-67136-9
DOIs	https://doi.org/10.1007/978-3-319-67137-6_41
Publication status	Published - 30 Sept 2017

Publication series

Name	Advances in Intelligent Systems and Computing
Volume	648
ISSN (Print)	2194-5357
ISSN (Electronic)	2194-5365

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science

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10.1007/978-3-319-67137-6_41

Cite this

Sun, L., Dbouk, H., Neumann, I., Schön, S., & Kreinovich, V. (2017). Taking into Account Interval (and Fuzzy) Uncertainty Can Lead to More Adequate Statistical Estimates. In Fuzzy Logic in Intelligent System Design: theory and applications (pp. 371-381). (Advances in Intelligent Systems and Computing; Vol. 648). Springer Verlag. https://doi.org/10.1007/978-3-319-67137-6_41

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abstract = "Traditional statistical data processing techniques (such as Least Squares) assume that we know the probability distributions of measurement errors. Often, we do not have full information about these distributions. In some cases, all we know is the bound of the measurement error; in such cases, we can use known interval data processing techniques. Sometimes, this bound is fuzzy; in such cases, we can use known fuzzy data processing techniques. However, in many practical situations, we know the probability distribution of the random component of the measurement error and we know the upper bound on the measurement error{\textquoteright}s systematic component. For such situations, no general data processing technique is currently known. In this paper, we describe general data processing techniques for such situations, and we show that taking into account interval and fuzzy uncertainty can lead to more adequate statistical estimates.",

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Taking into Account Interval (and Fuzzy) Uncertainty Can Lead to More Adequate Statistical Estimates. / Sun, Ligang; Dbouk, Hani; Neumann, Ingo et al.
Fuzzy Logic in Intelligent System Design: theory and applications. Springer Verlag, 2017. p. 371-381 (Advances in Intelligent Systems and Computing; Vol. 648).

Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review

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T1 - Taking into Account Interval (and Fuzzy) Uncertainty Can Lead to More Adequate Statistical Estimates

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AU - Kreinovich, Vladik

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AB - Traditional statistical data processing techniques (such as Least Squares) assume that we know the probability distributions of measurement errors. Often, we do not have full information about these distributions. In some cases, all we know is the bound of the measurement error; in such cases, we can use known interval data processing techniques. Sometimes, this bound is fuzzy; in such cases, we can use known fuzzy data processing techniques. However, in many practical situations, we know the probability distribution of the random component of the measurement error and we know the upper bound on the measurement error’s systematic component. For such situations, no general data processing technique is currently known. In this paper, we describe general data processing techniques for such situations, and we show that taking into account interval and fuzzy uncertainty can lead to more adequate statistical estimates.

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Taking into Account Interval (and Fuzzy) Uncertainty Can Lead to More Adequate Statistical Estimates

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