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
Challenges in stochastic programming
Mathematical Programming: Series A and B
Chance constrained programming with fuzzy parameters
Fuzzy Sets and Systems
Fuzzy multiple level programming
Applied Mathematics and Computation
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
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In this paper, we focus on two-level linear programming problems involving random variable coefficients in objective functions and constraints. According to the concept of chance constrained programming, the two-level stochastic linear programming problems are transformed into deterministic ones through the expectation optimization model and the variance minimization model. After introducing fuzzy goals for objective functions, interactive fuzzy programming to derive a satisfactory solution for decision makers is presented as a fusion of stochastic approach and fuzzy one. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.