Robust solutions with fuzzy linear chance constrained programming

It is well known that optimization problems should consider the uncertainty of the input information to attain robust solutions. Although probability theory is the most extended uncertainty model, when input data are expressed in vague or fuzzy terms, or when statistical information is not available, possibility theory arises as a very suitable uncertainty model. This paper proposes two different criteria to obtain robust solutions for linear optimization problems when the objective coefficients are modeled with possibility distributions. Chance constrained programming is used, leading to equivalent crisp optimization problems, which can be solved by commercial optimization software. A case example is described to illustrate the use of the proposed approach.