Linear programming with interval type-2 fuzzy right hand side parameters

This paper presents a general method to handle uncertainty to the Right Hand Side parameters of a Linear Programming (LP) model by means of Interval Type-2 Fuzzy Sets (IT2 FS) and trapezoidal membership functions. Fuzzy Linear Programming (FLP) is a recent approach used on many situations where its optimal solution is provided by classical techniques as Simplex and Karmarkar algorithms. In this proposal, a LP problem with uncertain Right Side parameters treated as Interval Type-2 Fuzzy sets is solved by two optimization strategies. After the IT2 FS inference process, a real-valued solution should be found. In this way two methods are proposed to obtain optimal solutions when uncertain right hand side parameters exist, based on an alpha-cut optimality criterion.