Linear Programming with fuzzy joint parameters: A Cumulative Membership Function approach

Abstract

This paper shows an alternative methodology to find optimal solutions of a Linear Programming problem defined in a fuzzy environment. The classical Fuzzy Linear Programming (FLP) problem is treated by using fuzzy restrictions in the form Ax b where˘indicates a Type-1 Fuzzy Set (T1 FS). The proposed approach uses jointȂ andb fuzzy parameters to solve a linear programming model under uncertainty conditions. Triangular fuzzy sets are used to reduce the computational complexity of the model, however other types of fuzzy sets can be used. A Cumulative Membership Function (CMF) approach is defined, some optimality conditions are discussed and a new theorem is proved. Finally a small example is provided.

FRand: MATLAB Toolbox for Fuzzy Random Number Simulation

“…where x ∈ R. Its fuzzy version is as follows (see Figueroa-García & López-Bello [2], [3], Figueroa-García [1] and Pulido-López et.al [12]).…”

“…Analogous concepts for fuzzy numbers have been proposed by Varón-Gaviria et al [14] and Pulido-López et al [12] who used the well known α-cuts representation of a fuzzy set and the cumulative membership function ψ A (x) of A (see Figueroa-García & López-Bello [2], [3] and Figueroa-García [1]). This way, it is possible to efficiently generate random variables using uniform random numbers and fuzzy sets easy to implement in general purpose code/software like MATLAB.…”