In this paper, we propose an interactive method for solving the multilevel linear programming problems based on the intuitionistic fuzzy set theory. Firstly, the membership function and the non-membership function are...In this paper, we propose an interactive method for solving the multilevel linear programming problems based on the intuitionistic fuzzy set theory. Firstly, the membership function and the non-membership function are introduced to describe the uncertainty of the decision makers. Secondly, a satisfactory solution is derived by updating the minimum satisfactory degrees with considerations of the overall satisfactory balance among all levels. In addition, the steps of the proposed method are given in this paper. Finally, numerical examples illustrate the feasibility of this method.展开更多
This paper considers multiobjective integer programming problems involving random variables in constraints. Using the concept of simple recourse, the formulated multiobjective stochastic simple recourse problems are t...This paper considers multiobjective integer programming problems involving random variables in constraints. Using the concept of simple recourse, the formulated multiobjective stochastic simple recourse problems are transformed into deterministic ones. For solving transformed deterministic problems efficiently, we also introduce genetic algorithms with double strings for nonlinear integer programming problems. Taking into account vagueness of judgments of the decision maker, an interactive fuzzy satisficing method is presented. In the proposed interactive method, after determineing the fuzzy goals of the decision maker, a satisficing solution for the decision maker is derived efficiently by updating the reference membership levels of the decision maker. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.展开更多
Multiobjective Programming (MOP) has become famous among many researchers due to more practical and realistic applications. A lot of methods have been proposed especially during the past four decades. In this paper, w...Multiobjective Programming (MOP) has become famous among many researchers due to more practical and realistic applications. A lot of methods have been proposed especially during the past four decades. In this paper, we develop a new algorithm based on a new approach to solve MOP by starting from a utopian point, which is usually infeasible, and moving towards the feasible region via stepwise movements and a simple continuous interaction with decision maker. We consider the case where all objective functions and constraints are linear. The implementation of the pro-posed algorithm is demonstrated by two numerical examples.展开更多
基金Supported by the National Natural Science Foundation of China(71471140,71171150,71103135)
文摘In this paper, we propose an interactive method for solving the multilevel linear programming problems based on the intuitionistic fuzzy set theory. Firstly, the membership function and the non-membership function are introduced to describe the uncertainty of the decision makers. Secondly, a satisfactory solution is derived by updating the minimum satisfactory degrees with considerations of the overall satisfactory balance among all levels. In addition, the steps of the proposed method are given in this paper. Finally, numerical examples illustrate the feasibility of this method.
文摘This paper considers multiobjective integer programming problems involving random variables in constraints. Using the concept of simple recourse, the formulated multiobjective stochastic simple recourse problems are transformed into deterministic ones. For solving transformed deterministic problems efficiently, we also introduce genetic algorithms with double strings for nonlinear integer programming problems. Taking into account vagueness of judgments of the decision maker, an interactive fuzzy satisficing method is presented. In the proposed interactive method, after determineing the fuzzy goals of the decision maker, a satisficing solution for the decision maker is derived efficiently by updating the reference membership levels of the decision maker. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.
文摘Multiobjective Programming (MOP) has become famous among many researchers due to more practical and realistic applications. A lot of methods have been proposed especially during the past four decades. In this paper, we develop a new algorithm based on a new approach to solve MOP by starting from a utopian point, which is usually infeasible, and moving towards the feasible region via stepwise movements and a simple continuous interaction with decision maker. We consider the case where all objective functions and constraints are linear. The implementation of the pro-posed algorithm is demonstrated by two numerical examples.
