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Maximin and maximal solutions for linear programming problems with possibilistic uncertainty

Erik Quaeghebeur (UGent) , Nathan Huntley (UGent) , Keivan Shariatmadar and Gert de Cooman (UGent)
(2012) Communications in Computer and Information Science. 299(4). p.430-439
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Abstract
We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possi-bility 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 uncer-tainty. We provide expressions for and illustrations of the maximin and maximal solutions of these decision problems and present computational approaches for dealing with them.
Keywords
maximality, maximinity, decision making, imprecise probabilities, coherent lower prevision, possibility distribution, vacuous lower prevision, linear program, interval uncertainty

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MLA
Quaeghebeur, Erik, et al. “Maximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty.” Communications in Computer and Information Science, edited by Salvatore Greco et al., vol. 299, no. 4, Springer, 2012, pp. 430–39, doi:10.1007/978-3-642-31718-7_45.
APA
Quaeghebeur, E., Huntley, N., Shariatmadar, K., & de Cooman, G. (2012). Maximin and maximal solutions for linear programming problems with possibilistic uncertainty. In S. Greco, B. Bouchon-Meunier, G. Coletti, M. Fedrizzi, B. Matarazzo, & R. R. Yager (Eds.), Communications in Computer and Information Science (Vol. 299, pp. 430–439). https://doi.org/10.1007/978-3-642-31718-7_45
Chicago author-date
Quaeghebeur, Erik, Nathan Huntley, Keivan Shariatmadar, and Gert de Cooman. 2012. “Maximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty.” In Communications in Computer and Information Science, edited by Salvatore Greco, Bernadette Bouchon-Meunier, Giulianella Coletti, Mario Fedrizzi, Benedetto Matarazzo, and Ronald R Yager, 299:430–39. Heidelberg, Germany: Springer. https://doi.org/10.1007/978-3-642-31718-7_45.
Chicago author-date (all authors)
Quaeghebeur, Erik, Nathan Huntley, Keivan Shariatmadar, and Gert de Cooman. 2012. “Maximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty.” In Communications in Computer and Information Science, ed by. Salvatore Greco, Bernadette Bouchon-Meunier, Giulianella Coletti, Mario Fedrizzi, Benedetto Matarazzo, and Ronald R Yager, 299:430–439. Heidelberg, Germany: Springer. doi:10.1007/978-3-642-31718-7_45.
Vancouver
1.
Quaeghebeur E, Huntley N, Shariatmadar K, de Cooman G. Maximin and maximal solutions for linear programming problems with possibilistic uncertainty. In: Greco S, Bouchon-Meunier B, Coletti G, Fedrizzi M, Matarazzo B, Yager RR, editors. Communications in Computer and Information Science. Heidelberg, Germany: Springer; 2012. p. 430–9.
IEEE
[1]
E. Quaeghebeur, N. Huntley, K. Shariatmadar, and G. de Cooman, “Maximin and maximal solutions for linear programming problems with possibilistic uncertainty,” in Communications in Computer and Information Science, Catania, Italy, 2012, vol. 299, no. 4, pp. 430–439.
@inproceedings{2090091,
  abstract     = {{We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possi-bility 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 uncer-tainty. We provide expressions for and illustrations of the maximin and maximal solutions of these decision problems and present computational approaches for dealing with them.}},
  author       = {{Quaeghebeur, Erik and Huntley, Nathan and Shariatmadar, Keivan and de Cooman, Gert}},
  booktitle    = {{Communications in Computer and Information Science}},
  editor       = {{Greco, Salvatore and Bouchon-Meunier, Bernadette and Coletti, Giulianella and Fedrizzi, Mario and Matarazzo, Benedetto and Yager, Ronald R}},
  isbn         = {{9783642317170}},
  issn         = {{1865-0929}},
  keywords     = {{maximality,maximinity,decision making,imprecise probabilities,coherent lower prevision,possibility distribution,vacuous lower prevision,linear program,interval uncertainty}},
  language     = {{eng}},
  location     = {{Catania, Italy}},
  number       = {{4}},
  pages        = {{430--439}},
  publisher    = {{Springer}},
  title        = {{Maximin and maximal solutions for linear programming problems with possibilistic uncertainty}},
  url          = {{http://doi.org/10.1007/978-3-642-31718-7_45}},
  volume       = {{299}},
  year         = {{2012}},
}
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