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Maximin and maximal solutions for linear programming problems with possibilistic uncertainty

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Project
IWT SBO project 60043, “Fuzzy Finite Element Method”
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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Citation

Please use this url to cite or link to this publication:

Chicago
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. Salvatore Greco, Bernadette Bouchon-Meunier, Giulianella Coletti, Mario Fedrizzi, Benedetto Matarazzo, and Ronald R Yager, 299:430–439. Heidelberg, Germany: Springer.
APA
Quaeghebeur, E., Huntley, N., Shariatmadar, K., & De Cooman, G. (2012). Maximin and maximal solutions for linear programming problems with possibilistic uncertainty. In Salvatore 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). Presented at the 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU - 2012), Heidelberg, Germany: Springer.
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.
MLA
Quaeghebeur, Erik, Nathan Huntley, Keivan Shariatmadar, et al. “Maximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty.” Communications in Computer and Information Science. Ed. Salvatore Greco et al. Vol. 299. Heidelberg, Germany: Springer, 2012. 430–439. Print.
@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},
  keyword      = {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://dx.doi.org/10.1007/978-3-642-31718-7\_45},
  volume       = {299},
  year         = {2012},
}

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