Robust and optimal control
Combinatorial optimization: current successes and directions for the future
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Interval Constraint Logic Programming
Selected Papers from Constraint Programming: Basics and Trends
Probability and Random Processes for Electrical and Computer Engineers
Probability and Random Processes for Electrical and Computer Engineers
Certainty closure: Reliable constraint reasoning with incomplete or erroneous data
ACM Transactions on Computational Logic (TOCL)
Qualitative spatial relationships for image interpretation by using a conceptual graph
Image and Vision Computing
Mixed constraint satisfaction: a framework for decision problems under incomplete knowledge
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Robust solutions of uncertain linear programs
Operations Research Letters
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Interval coefficients have been introduced in OR and CP to specify uncertain data in order to provide reliable solutions to convex models. The output is generally a solution set, guaranteed to contain all solutions possible under any realization of the data. This set can be too large to be meaningful. Furthermore, each solution has equal uncertainty weight, thus does not reflect any possible degree of knowledge about the data. To overcome these problems we propose to extend the notion of interval coefficient by introducing a second dimension to each interval bound. Each bound is now specified by its data value and its degree of knowledge. This is formalized using the cumulative distribution function of the data set. We define the formal framework of constraint reasoning over this cdf-intervals. The main contribution of this paper concerns the formal definition of a new interval arithmetic and its implementation. Promising results on problem instances demonstrate the approach.