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https://knowledgecommons.lakeheadu.ca/handle/2453/2439
Title: | Set-based computations |
Authors: | Noroozi, Nasser |
Keywords: | Set theory |
Issue Date: | 1995 |
Abstract: | The representation of uncertain information and inference with such information are some of the fundamental issues in uncertainty management. Conventional methods for uncertainty management usually use a single value with the exception of interval-based approaches. In interval-based approaches, an interval is used to represent the uncertain information. It is assumed that the true, possibly unknown, value lies in an interval. However, in order to use interval-based methods, there must exist an order relation on the set of data values. The main objective of this thesis is to extend single-valued and interval-valued methods by introducing a framework of set-valued computations. In this model, uncertain information is described by a set without any further restrictions. Basic issues of set-based computations are investigated. Operations on set values are defined based on the corresponding point-based (i.e., single-value-based) operations on their members. The properties of set-based computations are examined in connection to the corresponding properties of the point-based computations. Within the proposed framework, a critical analysis of a number of existing set-based computation methods is presented. This provides further evidence supporting the proposed model. To a large extent, the present study may be regarded as a more explicit re-examination of methods that have been implicitly used in many studies, using a unified notion. The results of such an investigation will be useful in establishing a framework for more systematic study of set-based computations. |
URI: | http://knowledgecommons.lakeheadu.ca/handle/2453/2439 |
metadata.etd.degree.discipline: | Mathematical Sciences |
metadata.etd.degree.name: | Master of Science |
metadata.etd.degree.level: | Master |
metadata.dc.contributor.advisor: | Yao, Yiyu |
Appears in Collections: | Retrospective theses |
Files in This Item:
File | Description | Size | Format | |
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NorooziN1995m-1b.pdf | 1.62 MB | Adobe PDF | View/Open |
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