Advances in Operations Research
Volume 2012 (2012), Article ID 635282, 13 pages
Research Article

Probabilistic Quadratic Programming Problems with Some Fuzzy Parameters

Department of Mathematics, Indian Institute of Technology, Kharagpur, Kharagpur 721 302, India

Received 11 October 2011; Revised 9 December 2011; Accepted 20 December 2011

Academic Editor: Shangyao Yan

Copyright © 2012 S. K. Barik and M. P. Biswal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a solution procedure for a quadratic programming problem with some probabilistic constraints where the model parameters are either triangular fuzzy number or trapezoidal fuzzy number. Randomness and fuzziness are present in some real-life situations, so it makes perfect sense to address decision making problem by using some specified random variables and fuzzy numbers. In the present paper, randomness is characterized by Weibull random variables and fuzziness is characterized by triangular and trapezoidal fuzzy number. A defuzzification method has been introduced for finding the crisp values of the fuzzy numbers using the proportional probability density function associated with the membership functions of these fuzzy numbers. An equivalent deterministic crisp model has been established in order to solve the proposed model. Finally, a numerical example is presented to illustrate the solution procedure.