An interval‐coefficient fuzzy binary linear programming, the solution, and its application under uncertainties

The common difficulty in solving a Binary Linear Programming (BLP) problem is uncertainties in the parameters and the model structure. The previous studies of BLP problems normally focus on parameter uncertainty or model structure uncertainty, but not on both types of uncertainties. This paper develops an interval‐coefficient Fuzzy Binary Linear Programming (IFBLP) and its solution for BLP problems under uncertainties both on parameters and model structure. In the IFBLP, the parameter uncertainty is represented by the interval coefficients, and the model structure uncertainty is reflected by the fuzzy constraints and a fuzzy goal. A novel and efficient methodology is used to solve the IFLBP into two extreme crisp‐coefficient BLPs, which are called the ‘best optimum model’ and the ‘worst optimum model’. The results of these two crisp‐coefficient extreme models can bound all outcomes of the IFBLP. One of the contributions in this paper is that it provides a mathematical sound approach (based on some mathematical developments) to find the boundaries of optimal alpha values, so that the linearity of model can be maintained during the conversions. The proposed approach is applied to a traffic noise control plan to demonstrate its capability of dealing with uncertainties.