Concepts for Decision Making under Severe Uncertainty with Partial Ordinal and Partial Cardinal Preferences

Christoph Jansen, Georg Schollmeyer, Thomas Augustin
Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:181-192, 2017.

Abstract

We introduce three different approaches for decision making under uncertainty, if (I) there is only partial (both cardinal and ordinal) information on an agent’s preferences and (II) the uncertainty about the states of nature is described by a credal set. Particularly, (I) is modeled by a pair of relations, one specifying the partial rank order of the alternatives and the other modeling partial information on the strength of preference. Our first approach relies on criteria that construct complete rankings of the acts based on generalized expectation intervals. Subsequently, we introduce different concepts of global admissibility that construct partial orders by comparing all acts simultaneously. Finally, we define criteria induced by suitable binary relations on the set of acts and, therefore, can be understood as concepts of local admissibility. Whenever suitable, we provide linear programming based algorithms for checking optimality/admissibility of acts.

Cite this Paper

BibTeX
@InProceedings{pmlr-v62-jansen17a, title = {Concepts for Decision Making under Severe Uncertainty with Partial Ordinal and Partial Cardinal Preferences}, author = {Jansen, Christoph and Schollmeyer, Georg and Augustin, Thomas}, booktitle = {Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {181--192}, year = {2017}, editor = {Antonucci, Alessandro and Corani, Giorgio and Couso, Inés and Destercke, Sébastien}, volume = {62}, series = {Proceedings of Machine Learning Research}, month = {10--14 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v62/jansen17a/jansen17a.pdf}, url = {https://proceedings.mlr.press/v62/jansen17a.html}, abstract = {We introduce three different approaches for decision making under uncertainty, if (I) there is only partial (both cardinal and ordinal) information on an agent’s preferences and (II) the uncertainty about the states of nature is described by a credal set. Particularly, (I) is modeled by a pair of relations, one specifying the partial rank order of the alternatives and the other modeling partial information on the strength of preference. Our first approach relies on criteria that construct complete rankings of the acts based on generalized expectation intervals. Subsequently, we introduce different concepts of global admissibility that construct partial orders by comparing all acts simultaneously. Finally, we define criteria induced by suitable binary relations on the set of acts and, therefore, can be understood as concepts of local admissibility. Whenever suitable, we provide linear programming based algorithms for checking optimality/admissibility of acts.} }
Endnote
%0 Conference Paper %T Concepts for Decision Making under Severe Uncertainty with Partial Ordinal and Partial Cardinal Preferences %A Christoph Jansen %A Georg Schollmeyer %A Thomas Augustin %B Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2017 %E Alessandro Antonucci %E Giorgio Corani %E Inés Couso %E Sébastien Destercke %F pmlr-v62-jansen17a %I PMLR %P 181--192 %U https://proceedings.mlr.press/v62/jansen17a.html %V 62 %X We introduce three different approaches for decision making under uncertainty, if (I) there is only partial (both cardinal and ordinal) information on an agent’s preferences and (II) the uncertainty about the states of nature is described by a credal set. Particularly, (I) is modeled by a pair of relations, one specifying the partial rank order of the alternatives and the other modeling partial information on the strength of preference. Our first approach relies on criteria that construct complete rankings of the acts based on generalized expectation intervals. Subsequently, we introduce different concepts of global admissibility that construct partial orders by comparing all acts simultaneously. Finally, we define criteria induced by suitable binary relations on the set of acts and, therefore, can be understood as concepts of local admissibility. Whenever suitable, we provide linear programming based algorithms for checking optimality/admissibility of acts.
APA
Jansen, C., Schollmeyer, G. & Augustin, T.. (2017). Concepts for Decision Making under Severe Uncertainty with Partial Ordinal and Partial Cardinal Preferences. Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 62:181-192 Available from https://proceedings.mlr.press/v62/jansen17a.html.

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