Fuzzy Nonlinear Programming with Single or Multiple Objective Functions

Abstract

In this chapter, being a nonlinear generalization of the previous one, nonlinear programming with single or multiple objective functions in a fuzzy environment is discussed. Firstly, nonlinear programming with a fuzzy goal and/or fuzzy constraints is briefly presented. Then multiobjective nonlinear programming and interactive multiobjective nonlinear programming, both incorporating fuzzy goals of the decision maker (DM), are explained in detail by putting special emphasis on the extended definition Pareto optimality. Finally, attention is focused on multiobjective nonlinear programming problems with fuzzy parameters (coefficients), which reflect the experts’ ambiguous or fuzzy understanding of the nature of the parameters in the problem-formulation process. By extend ing the usual Pareto optimality concepts, interactive decision-making methods, both without and with the fuzzy goals of the DM, for deriving a satisficing solution from an extended Pareto optimal solution set are presented.