Abstract
This paper considers two-level integer programming problems involving random fuzzy variables with cooperative behavior of the decision makers. Considering the probabilities that the decision makers’ objective function values are smaller than or equal to target variables, fuzzy goals of the decision makers are introduced. Using the fractile criteria to optimize the target variables under the condition that the degrees of possibility with respect to the attained probabilities are greater than or equal to certain permissible levels, the original random fuzzy two-level integer programming problems are reduced to deterministic ones. Through the introduction of genetic algorithms with double strings for nonlinear integer programming problems, interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example demonstrates the feasibility and efficiency of the proposed method.
Highlights
Decision making problems in hierarchical managerial or public organizations are often formulated as two-level mathematical programming problems [1,2]
In order to overcome the problem in their methods, by eliminating the fuzzy goals for the decision variables, Sakawa et al have proposed interactive fuzzy programming for two-level or multi-level linear programming problems to obtain a satisfactory solution for decision makers [8,9]
For tackling cooperative decision making problems in hierarchical organizations under random fuzzy environments, we introduced fuzzy two-level integer programming problems involving random fuzzy variables
Summary
Decision making problems in hierarchical managerial or public organizations are often formulated as two-level mathematical programming problems [1,2]. From a viewpoint of ambiguity and randomness different from fuzzy random variables [20,21,22], by considering the experts’ ambiguous understanding of means and variances of random variables, a concept of random fuzzy variables was proposed, and mathematical programming problems with random fuzzy variables were formulated together with the development of a simulation-based approximate solution method [24] Under these circumstances, as a first attempt to tackle decision making problems in hierarchical organizations under random fuzzy environments, assuming cooperative behavior of the decision makers, we have formulated random fuzzy two-level linear programming problems [25]. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method
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