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/}
}