Short rational generating functions for solving some families of fuzzy integer programming problems

On the fuzzy maximal covering location problem

“…Depending on the characteristics of the problem and involved data, several alternatives can be used for incorporating fuzzy information within a mathematical programming model, as already discussed in [22]. Explicit considerations for FILP have been discussed in [20] and the complexity of these models studied in [7]. As a generalization of FILP, fuzzy mixed-integer linear programming (FMILP) incorporates fuzzy continuous decision variables to the formulations of the problems.…”

“…Approaches for handling models with integer or binary variables have also been studied (see, e.g. [20,21]), including specific frameworks for some fuzzy programmes [2], as well as complexity results [7]. In fact, the MCLP has already been studied from a fuzzy perspective.…”

“…Nevertheless, we will see that it is enough to consider the crisp counterpart of such variables. Following the methodology used with other problems dealing with fuzzy objectives [2,7,20], for solving our model we operate on an equivalent mixed-binary linear multiobjective formulation. In search of compromise solutions for that problem, i.e., Pareto solutions whose objective values are as close as possible to the ideal point, we propose a solution algorithm based on the augmented weighted Tchebycheff method, which produces solutions of guaranteed Pareto optimality (see, e.g.…”

On a fully fuzzy framework for minimax mixed integer linear programming

“…Concerning the complexity, FFLP is NP-hard, since its crisp version is. However, in [9] it is proved that if the fuzzy numbers involved in the problem are totally described by a finite ranking system, certain encoding of the solutions can be found in polynomial-time when the number of integer variables is fixed, and the solutions can be enumerated using a polynomial delay algorithm.…”