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A Unified Framework for Indeterminate Probabilities and Utilities
Stockholm University, Faculty of Science, Department of Mathematics.
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In classic decision theory, the different alternatives in a decision situation are merely objects of choice, and it is assumed that a decision maker can assign precise numerical values corresponding to the true value of each consequence, as well as precise numerical probabilities for their occurrences. However, in real-life situations, the ordering of alternatives from most to least preferred is often a delicate matter and an adequate mathematical representation is crucial. In attempting to address real-life problems, where uncertainty about data prevails, some kind of representation of imprecise information is important and several have been proposed. In particular, 1st order representations, such as sets of probability measures, upper and lower probabilities as well as interval probabilities and utilities of various kinds, have been suggested for enabling a better representation of the input sentences for a subsequent decision analysis. There are, however, problems with all the above approaches that are difficult to discuss in their own terminology.

This thesis presents a family of methods and procedures for representing and analysing imprecise, vague, and incomplete probabilistic decision and risk problems. In particular, we suggest methods for stating and analysing probabilities and values (utilities) with belief distributions over them as well as optimization procedures for fast evaluation of decision rules with respect to such statements. We have extended the classical risk and decision evaluation process by the integration of procedures for handling qualitative, vague, and numerically imprecise probabilities and utilities. The shortcomings of the principle of maximising the expected utility, and of utility theory in general, have in part been compensated for by the introduction of various kinds of alternative decision rules. We have given a theoretical motivation for the methodology required for such evaluations involving vague and numerically imprecise data. There is also a need for a general discussion of interval decision methods, and such a discussion is included using an analytic method based on higher-order representations (e.g. a distribution over a probability distribution). A side effect is that the representation capability has increased by the inclusion of distributions over classes of probability and utility measures over sets of outcomes. Regarding this, we have investigated how local distributions, i.e. distributions over projections, can be derived from global distributions and investigated consistency measures expressing the extent into which user-asserted local distributions can be used for defining global distributions. The approach provides a decision-maker with the means for expressing varying degrees of imprecision in the input sentences.

Place, publisher, year, edition, pages
Stockholm: Matematiska institutionen , 2005. , 138 p.
Keyword [en]
Decision Analysis, Risk Analysis, Second order probabilities
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-358ISBN: 91-7155-009-7 (print)OAI: oai:DiVA.org:su-358DiVA: diva2:192910
Public defence
2005-03-03, sal 14, hus 5, Kräftriket, Stockholm, 10:00
Opponent
Supervisors
Available from: 2005-02-08 Created: 2005-02-08Bibliographically approved
List of papers
1. A Framework for Analysing Decisions under Risk
Open this publication in new window or tab >>A Framework for Analysing Decisions under Risk
1998 In: European Journal of Operational Research, ISSN 0377-2217, Vol. 104, no 3, 474–484- p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-23570 (URN)
Note
Part of urn:nbn:se:su:diva-358Available from: 2005-02-08 Created: 2005-02-08Bibliographically approved
2. The Logic of Conflicts between Decision Making Agents
Open this publication in new window or tab >>The Logic of Conflicts between Decision Making Agents
2000 In: Journal of Logic and Computation, ISSN 0955-792X, Vol. 10, no 4, 583–602- p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-23571 (URN)
Note
Part of urn:nbn:se:su:diva-358Available from: 2005-02-08 Created: 2005-02-08Bibliographically approved
3. Risk Constraints in Agent Based Decisions
Open this publication in new window or tab >>Risk Constraints in Agent Based Decisions
2000 In: Encyclopedia of Computer Science and Technology, Marcel Dekker Inc , 2000, 263–280- p.Chapter in book (Other academic) Published
Place, publisher, year, edition, pages
Marcel Dekker Inc, 2000
Identifiers
urn:nbn:se:su:diva-23572 (URN)
Note
Part of urn:nbn:se:su:diva-358Available from: 2005-02-08 Created: 2005-02-08Bibliographically approved
4. Second-Order Decision Analysis
Open this publication in new window or tab >>Second-Order Decision Analysis
2001 In: International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, ISSN 0218-4885, Vol. 9, no 1, 13-37 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-23573 (URN)
Note
Part of urn:nbn:se:su:diva-358Available from: 2005-02-08 Created: 2005-02-08Bibliographically approved
5. Decision Analysis with Kripke Semantics
Open this publication in new window or tab >>Decision Analysis with Kripke Semantics
2002 In: Proceedings of IEEE IS, 2002, 151–156- p.Chapter in book (Other academic) Published
Identifiers
urn:nbn:se:su:diva-23574 (URN)
Note
Part of urn:nbn:se:su:diva-358Available from: 2005-02-08 Created: 2005-02-08Bibliographically approved
6. Value Differences using Second Order Distributions
Open this publication in new window or tab >>Value Differences using Second Order Distributions
2005 In: International Journal of Approximate Reasoning, ISSN 0888-613X, Vol. 38, no 1, 81–97- p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-23575 (URN)
Note
Part of urn:nbn:se:su:diva-358Available from: 2005-02-08 Created: 2005-02-08Bibliographically approved

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Citation style
  • apa
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Output format
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