Fuzzy Multiobjective 0–1 Programming

In this chapter, as a natural extension of single-objective 0–1 programming problems discussed in the previous chapter, multiobjective 0–1 programming problems are formulated by assuming that the decision maker may have a fuzzy goal for each of the objective functions. Through the combination of the desirable features of both the interactive fuzzy satisficing methods for continuous variables and the genetic algorithms with double strings (GADS) discussed in the previous chapter, an interactive fuzzy satisficing method to derive a satisficing solution for the decision maker is presented. Furthermore, by considering the experts’ imprecise or fuzzy understanding of the nature of the parameters in the problem-formulation process, the multiobjective 0–1 programming problems involving fuzzy parameters are formulated. Through the introduction of extended Pareto optimality concepts, an interactive decision-making method for deriving a satisficing solution of the decision maker from among the extended Pareto optimal solution set is presented together with detailed numerical examples.