A novel method for decision making with fuzzy probability assessments and fuzzy payoff is presented. The consistency of the fuzzy probability assessment is considered. A fuzzy aggregate algorithm is used to indicate t...A novel method for decision making with fuzzy probability assessments and fuzzy payoff is presented. The consistency of the fuzzy probability assessment is considered. A fuzzy aggregate algorithm is used to indicate the fuzzy expected payoff of alternatives. The level sets of each fuzzy expected payoff are then obtained by solving linear programming models. Based on a defuzzification function associated with the level sets of fuzzy number and a numerical integration formula (Newton-Cotes formula), an effective approach to rank the fuzzy expected payoff of alternatives is also developed to determine the best alternative. Finally, a numerical example is provided to illustrate the proposed method.展开更多
In this paper, we consider multiobjective two-person zero-sum games with vector payoffs and vector fuzzy payoffs. We translate such games into the corresponding multiobjective programming problems and introduce the pe...In this paper, we consider multiobjective two-person zero-sum games with vector payoffs and vector fuzzy payoffs. We translate such games into the corresponding multiobjective programming problems and introduce the pessimistic Pareto optimal solution concept by assuming that a player supposes the opponent adopts the most disadvantage strategy for the self. It is shown that any pessimistic Pareto optimal solution can be obtained on the basis of linear programming techniques even if the membership functions for the objective functions are nonlinear. Moreover, we propose interactive algorithms based on the bisection method to obtain a pessimistic compromise solution from among the set of all pessimistic Pareto optimal solutions. In order to show the efficiency of the proposed method, we illustrate interactive processes of an application to a vegetable shipment problem.展开更多
文摘A novel method for decision making with fuzzy probability assessments and fuzzy payoff is presented. The consistency of the fuzzy probability assessment is considered. A fuzzy aggregate algorithm is used to indicate the fuzzy expected payoff of alternatives. The level sets of each fuzzy expected payoff are then obtained by solving linear programming models. Based on a defuzzification function associated with the level sets of fuzzy number and a numerical integration formula (Newton-Cotes formula), an effective approach to rank the fuzzy expected payoff of alternatives is also developed to determine the best alternative. Finally, a numerical example is provided to illustrate the proposed method.
文摘In this paper, we consider multiobjective two-person zero-sum games with vector payoffs and vector fuzzy payoffs. We translate such games into the corresponding multiobjective programming problems and introduce the pessimistic Pareto optimal solution concept by assuming that a player supposes the opponent adopts the most disadvantage strategy for the self. It is shown that any pessimistic Pareto optimal solution can be obtained on the basis of linear programming techniques even if the membership functions for the objective functions are nonlinear. Moreover, we propose interactive algorithms based on the bisection method to obtain a pessimistic compromise solution from among the set of all pessimistic Pareto optimal solutions. In order to show the efficiency of the proposed method, we illustrate interactive processes of an application to a vegetable shipment problem.
