Date of Award

2011-01-01

Degree Name

Master of Science

Department

Computer Science

Advisor(s)

Vladik Kreinovich

Abstract

In many practical situations, we have a sample of objects of a given type. When we measure the values of a certain quantity x for these objects, we get a sequence of values x1, . . . , xn. When the sample is large enough, then the arithmetic mean E of the values xi is a good approximation for the average value of this quantity for all the objects from this class. Other expressions provide a good approximation to statistical characteristics such as variance, covariance, and correlation.

The values xi come from measurements, and measurement is never absolutely accurate.

Often, the only information that we have about the measurement error is the upper bound ∆i on this error. In this case, once we have the measurement result x􏰈i, the condition def |x􏰈i − xi| ≤ ∆i implies that the actual (unknown) value xi belongs to the interval xi = [x􏰈i − ∆i, x􏰈i + ∆i]. Different values xi ∈ xi from the corresponding intervals lead, in general, to different values of sample mean, sample variance, etc. It is therefore desirable to find the range of possible values of these characteristics when xi ∈ xi.

It is known that evaluating such ranges is, in general, NP-hard. The main objective of this thesis is to design feasible (i.e., polynomial-time) algorithms for practically important situations. Several such algorithms are described and proved to be correct.

Language

en

Provenance

Received from ProQuest

File Size

59 pages

File Format

application/pdf

Rights Holder

Ali Jalal-Kamali

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