Linear programming with fuzzy random variable coefficients
Fuzzy Sets and Systems
Hierarchical optimization: a satisfactory solution
Fuzzy Sets and Systems
Fuzzy approach for multi-level programming problems
Computers and Operations Research
Fuzzy Sets and Systems - Special issue on soft decision analysis
Fuzzy multiple level programming
Applied Mathematics and Computation
Random fuzzy dependent-chance programming and its hybrid intelligent algorithm
Information Sciences—Informatics and Computer Science: An International Journal
Interactive fuzzy programming for decentralized two-level linear programming problems
Fuzzy Sets and Systems - Theme: Decision and optimization
Fuzzy Sets and Systems - Special issue: Optimization and decision support systems
Fuzzy programming approach to multi-level programming problems
Fuzzy Sets and Systems - Theme: Multicriteria decision
Interactive balance space approach for solving multi-level multi-objective programming problems
Information Sciences: an International Journal
Fuzzy Stochastic Multiobjective Programming
Fuzzy Stochastic Multiobjective Programming
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This paper focuses on interactive decision making methods for random fuzzy two-level linear programming problems. 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 model 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 programming problems are reduced to deterministic ones. Interactive fuzzy nonlinear programming to obtain 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.