Linear programming with fuzzy random variable coefficients
Fuzzy Sets and Systems
On fuzzy random linear programming
Fuzzy Sets and Systems
Fuzziness and randomness in an optimization framework
Fuzzy Sets and Systems
Hierarchical optimization: a satisfactory solution
Fuzzy Sets and Systems
Fuzzy approach for multi-level programming problems
Computers and Operations Research
On fuzzy stochastic optimization
Fuzzy Sets and Systems - Special issue on fuzzy optimization
Fuzzy Sets and Systems - Special issue on soft decision analysis
Genetic Algorithms and Fuzzy Multiobjective Optimization
Genetic Algorithms and Fuzzy Multiobjective Optimization
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 random chance-constrained programming
IEEE Transactions on Fuzzy Systems
Fuzzy random dependent-chance programming
IEEE Transactions on Fuzzy Systems
Interactive random fuzzy two-level programming through possibility-based probability model
Information Sciences: an International Journal
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In this paper, assuming cooperative behavior of the decision makers, two-level linear programming problems under fuzzy random environments are considered. To deal with the formulated fuzzy random two-level linear programming problems, @a-level sets of fuzzy random variables are introduced and an @a-stochastic two-level linear programming problem is defined for guaranteeing the degree of realization of the problem. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced and the @a-stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through probability maximization, the transformed stochastic two-level programming problem can be reduced to a deterministic one. 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 is provided to demonstrate the feasibility and efficiency of the proposed method.