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Maximin and maximal solutions for linear programming problems with possibilistic uncertainty

Erik Quaeghebeur UGent, Nathan Huntley UGent, Keivan Shariatmadar UGent and Gert De Cooman UGent (2012) Communications in Computer and Information Science. 299(4). p.430-439
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.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
maximinity, maximality, decision making, imprecise probabilities, coherent lower prevision, possibility distribution, vacuous lower prevision, linear program, interval uncertainty
in
Communications in Computer and Information Science
Commun. comput. inf. sci.
editor
Salvatore Greco, Bernadette Bouchon-Meunier, Giulianella Coletti, Mario Fedrizzi, Benedetto Matarazzo and Ronald R Yager
volume
299
issue
4
pages
430 - 439
publisher
Springer
place of publication
Heidelberg, Germany
conference name
14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU - 2012)
conference location
Catania, Italy
conference start
2012-07-09
conference end
2012-07-13
ISSN
1865-0929
ISBN
9783642317187
9783642317170
DOI
10.1007/978-3-642-31718-7_45
project
IWT SBO project 60043, “Fuzzy Finite Element Method”
language
English
UGent publication?
yes
classification
C1
copyright statement
I have transferred the copyright for this publication to the publisher
VABB id
c:vabb:339836
VABB type
VABB-5
id
2090091
handle
http://hdl.handle.net/1854/LU-2090091
date created
2012-04-18 09:51:27
date last changed
2012-08-10 14:55:39
@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         = {9783642317187},
  issn         = {1865-0929},
  keyword      = {maximinity,maximality,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},
}

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.