Title: An approach for linear programming under randomness and fuzziness: a case of discrete random variables with fuzzy probabilities

Authors: Maged G. Iskander

Addresses: Faculty of Business Administration, Economics and Political Science, The British University in Egypt, P.O. Box 43, El-Sherouk City 11837, Cairo, Egypt

Abstract: This paper presents a new approach for solving stochastic fuzzy linear programming problems. The random variables in the constraints and in the objective function are discrete with triangular fuzzy probabilities. The α-cut method is applied to the triangular membership functions of the fuzzy probabilities. For the constraints, the chance-constrained approach is utilised, whether according to strict dominance relation or dominance relation. The mean-variance criterion is exploited in the objective function, whereas four different cases are considered. The model, for the general case, which takes the form of mixed zero-one non-linear programme, is illustrated by a numerical example.

Keywords: stochastic fuzzy programming; discrete random variables; fuzzy probabilities; chance-constrained approach; mean variance criterion; chance constraints; stochastic programming.

DOI: 10.1504/IJOR.2012.048868

International Journal of Operational Research, 2012 Vol.15 No.2, pp.215 - 225

Published online: 11 Jan 2015 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article