Maximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty
We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possibility distributions. The uncertainty is given a behavioral interpretation using coherent lower previsions from the theory of imprecise probabilities. We give a meaning to the linear programming problems by reformulating them as decision problems under such imprecise-probabilistic uncertainty. We provide expressions for and illustrations of the maximin and maximal solutions of these decision problems and present computational approaches for dealing with them.
Keywordslinear program interval uncertainty vacuous lower prevision possibility distribution coherent lower prevision imprecise probabilities decision making maximinity maximality
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