Irrelevant Natural Extension for Choice Functions
Abstract
We consider coherent choice functions under the recent axiomatisation proposed by De Bock and De Cooman that guarantees a representation in terms of binary preferences, and we discuss how to define conditioning in this framework. In a multivariate context, we propose a notion of marginalisation, and its inverse operation called weak (cylindrical) extension. We combine this with our definition of conditioning to define a notion of irrelevance, and we obtain the irrelevant natural extension in this framework: the least informative choice function that satisfies a given irrelevance assessment.
Cite
Text
Van Camp and Miranda. "Irrelevant Natural Extension for Choice Functions." Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, 2019.Markdown
[Van Camp and Miranda. "Irrelevant Natural Extension for Choice Functions." Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, 2019.](https://mlanthology.org/isipta/2019/vancamp2019isipta-irrelevant/)BibTeX
@inproceedings{vancamp2019isipta-irrelevant,
title = {{Irrelevant Natural Extension for Choice Functions}},
author = {Van Camp, Arthur and Miranda, Enrique},
booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications},
year = {2019},
pages = {414-423},
volume = {103},
url = {https://mlanthology.org/isipta/2019/vancamp2019isipta-irrelevant/}
}