Fuzzy Goal Programming And Its Approximate Solution

In this paper, the models and approximate solutions of fuzzy goal programming problem were discussed. Firstly, the weighted additive model with preemptive priority to solve Fuzzy Goal Programming (FGP) is formulated based on the simple and weighted additive model and the simple additive model with preemptive priority; Secondly, according to FGP model with decision variables and goals and deviations being triangular fuzzy numbers, its equivalent model and iterative algorithm are proposed. Then the paper discusses the method of using linear function or staggered function or piecewise linear function to approximate nonlinear function in FGP problem and the concepts of its approximate model and approximate M-Pareto optimal solution, educe the relation of approximate solution and original solution and validity of this approximate method based on the sensibility analysis, propose dichotomy of piecewise approximate. The paper presents the method to judge linear function approximate nonlinear function with degree ε or not and prove that any nonlinear function can be approximated by piecewise linear function with finite piece.