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Multimodality, uncertainty and aggregation
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Brus, Tomek (1985) Multimodality, uncertainty and aggregation. PhD thesis, University of Warwick.
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WRAP_Theses_Brus_1985.pdf - Submitted Version - Requires a PDF viewer. Download (5Mb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b1445506~S15
Abstract
The prime purpose of this thesis is to devise a method for aggregating beliefs in decision situations involving conflict. In the process of conducting this investigation it has been found that a completely fresh approach to interpreting and modelling uncertainty is required.
The major mathematical tool employed throughout this work is Catastrophe Theory. The relevant aspects of this subject are presented in the first chapter and are repeatedly used in the three main sections of the thesis.
A considerable part of the work is concerned with the new way of eliciting statements about beliefs. A number of illustrations is included in order to provide an intuitive feel for this interpretation of probability. The proposed method gives a basis for an aggregation scheme. Catastrophe Theory provides the framework for constructing aggregation rules sensitive to aspects like conflict, grouping and precision of information. Some particular models are described in detail.
In another section the geometry of a certain type of mixtures is analysed. Mixtures can be used for modelling aggregation problems and their main properties are discussed.
| Item Type: | Thesis (PhD) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Catastrophes (Mathematics), Uncertainty -- Mathematical models, Aggregation operators | ||||
| Official Date: | June 1985 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Department of Statistics | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Harrison, P. J. | ||||
| Sponsors: | Sussex European Research Centre ; University of Warwick | ||||
| Format of File: | |||||
| Extent: | [vi], 156 leaves | ||||
| Language: | eng |
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