A branch and bound algorithm for the bilevel programming problem
SIAM Journal on Scientific and Statistical Computing
The theory of fuzzy stochastic processes
Fuzzy Sets and Systems
New branch-and-bound rules for linear bilevel programming
SIAM Journal on Scientific and Statistical Computing
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
On fuzzy stochastic optimization
Fuzzy Sets and Systems - Special issue on fuzzy optimization
Stackelberg solutions to multiobjective two-level linear programming problems
Journal of Optimization Theory and Applications
Genetic Algorithms and Fuzzy Multiobjective Optimization
Genetic Algorithms and Fuzzy Multiobjective Optimization
Global Optimization of Nonlinear Bilevel Programming Problems
Journal of Global Optimization
A Trust-Region Method for Nonlinear Bilevel Programming: Algorithm and Computational Experience
Computational Optimization and Applications
A Possibilistic and Stochastic Programming Approach to Fuzzy Random MST Problems*
IEICE - Transactions on Information and Systems
Parametric global optimisation for bilevel programming
Journal of Global Optimization
Information Sciences: an International Journal
Bilevel optimization applied to strategic pricing in competitive electricity markets
Computational Optimization and Applications
Information Sciences: an International Journal
Fuzzy random chance-constrained programming
IEEE Transactions on Fuzzy Systems
Fuzzy random dependent-chance programming
IEEE Transactions on Fuzzy Systems
Mathematical and Computer Modelling: An International Journal
Information Sciences: an International Journal
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This paper considers Stackelberg solutions for decision making problems in hierarchical organizations under fuzzy random environments. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced into the formulated fuzzy random two-level linear programming problems. On the basis of the possibility and necessity measures that each objective function fulfills the corresponding fuzzy goal, together with the introduction of probability maximization criterion in stochastic programming, we propose new two-level fuzzy random decision making models which maximize the probabilities that the degrees of possibility and necessity are greater than or equal to certain values. Through the proposed models, it is shown that the original two-level linear programming problems with fuzzy random variables can be transformed into deterministic two-level linear fractional programming problems. For the transformed problems, extended concepts of Stackelberg solutions are defined and computational methods are also presented. A numerical example is provided to illustrate the proposed methods.