Generalized fuzzy linear programming for decision making under uncertainty: Feasibility of fuzzy solutions and solving approach

• A generalized fuzzy linear programming (GFLP) method is proposed.
• The feasibility of fuzzy solutions for GFLP is proved.
• A stepwise interactive algorithm (SIA) is advanced to generate fuzzy solutions.
• A numerical example is used to illustrate the solution processes of GFLP.
• Comparison is conducted between solutions from SIA and Monte Carlo simulation.

In this study, a generalized fuzzy linear programming (GFLP) method is developed for dealing with uncertainties expressed as fuzzy sets. The feasibility of fuzzy solutions of the GFLP problem is investigated. A stepwise interactive algorithm (SIA) based on the idea of design of experiment is then advanced to solve the GFLP problem. This SIA method was implemented through (i) discretizing membership grade of fuzzy parameters into a finite number of α-cut levels, (ii) converting the GFLP model into an interval linear programming (ILP) submodel under every α-cut level, (iii) solving the ILP submodels through an interactive algorithm and obtaining the associated interval solutions, (iv) acquiring the membership functions of fuzzy solutions through statistical regression methods. A simple numerical example is then proposed to illustrate the solution process of the GFLP model through SIA. A comparison between the solutions obtained though SIA and Monte Carlo method is finally conducted to demonstrate the robustness of the SIA method. The results indicate that the membership functions for decision variables and objective function are reasonable and robust.