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. 1. Introduction In real-world applications, it is very much difficult to know all the information about the input parameters of the mathematical programming model because relevant data are inexistent or scarce, difficult to obtain or to estimate, the system is subject to changes, and so forth, that is, input parameters are uncertain. One of the best ways of modeling these uncertainties in the form of mathematical programming is known as stochastic programming. It is widely used in several research areas such as agriculture, capacity planning, finance, forestry, military, production control and scheduling, sport, telecommunications, transportation, environmental management planning. It should also be noted, that in many practical situations, knowledge about the data (i.e., the coefficients/parameters of the model) is not purely probabilistic or possibilistic but rather a mixture of both kinds. For an example consider a firm that desires to maximize its profit by meeting all the customers demands which fluctuate due to random change in price. By the stochasticity of the demand and the fact that the production may not fulfill all the possible demands, this point cannot be satisfactorily answered by the true or false statement. This optimization problem is related to two types of uncertainties, namely, randomness and fuzziness, which motivates the proposed study in this direction. Quadratic programming (QP) is an optimization technique where we minimize/maximize a quadratic objective function of several variables subject to a set of linear constraints. QP has a wide range of applications, such as portfolio selection, electrical energy production,
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