Optimization Problems With Fuzzy Relation Inequality Constraints

Five classes of optimization models are studied in this theses . Since the feasible domain of each model is in general non-convex, we apply various methods to solve them respectively. The first model is the optimization problems with s linear objective function subject to a system of fuzzy relation equations and a system of fuzzy relation inequalities, which are solved by using path method and 0-1 integer programming with branch and bound method. The second one is the latticized linear programming with a fuzzy lattice objective function subject to a system of fuzzy relation inequalities and equations, which are solved by adopting direct method, path method and 0-1 integer programming method. We apply tolerance approach and positive & negative ideal solution method to solve the third one where the fuzzy relation inequalities are fuzzy, i.e. there exists an acceptable tolerance. The fourth one is a kind of new possibilitic fuzzy linear programming. Comparison of fuzzy numbers, "cut-paste" method and positive & negative ideal solution method are introduced. In order to solve this kind of model, we design the procedure of Genetic algorithm according to stochastic simulation. The last one is the model with expected value which is transformed into the programming with crisp constraints coefficient by using expected value.