A general model for fuzzy linear programming
Fuzzy Sets and Systems
Linear programming problems and ranking of fuzzy numbers
Fuzzy Sets and Systems
A new approach to some possibilistic linear programming problems
Fuzzy Sets and Systems
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Ranking and defuzzification methods based on area compensation
Fuzzy Sets and Systems
Linear programming with fuzzy variables
Fuzzy Sets and Systems
Evolutionary algorithm solution to fuzzy problems: Fuzzy linear programming
Fuzzy Sets and Systems
Reasonable properties for the ordering of fuzzy quantities (II)
Fuzzy Sets and Systems
Fuzzy Mathematical Programming: Methods and Applications
Fuzzy Mathematical Programming: Methods and Applications
On duality in linear programming under fuzzy environment
Fuzzy Sets and Systems - Theme: Decision and optimization
Satisficing solutions and duality in interval and fuzzy linear programming
Fuzzy Sets and Systems - Special issue: Interfaces between fuzzy set theory and interval analysis
Duality in Fuzzy Linear Programming: Some New Concepts and Results
Fuzzy Optimization and Decision Making
Fuzzy Mathematical Programming and Fuzzy Matrix Games (Studies in Fuzziness and Soft Computing)
Fuzzy Mathematical Programming and Fuzzy Matrix Games (Studies in Fuzziness and Soft Computing)
The use of parametric programming in fuzzy linear programming
Fuzzy Sets and Systems
The solution and duality of imprecise network problems
Computers & Mathematics with Applications
Sensitivity analysis in fuzzy number linear programming problems
Mathematical and Computer Modelling: An International Journal
A Two-Fold Linear Programming Model with Fuzzy Data
International Journal of Fuzzy System Applications
International Journal of Fuzzy System Applications
Information Sciences: an International Journal
Fuzzy Optimization and Decision Making
A stepwise fuzzy linear programming model with possibility and necessity relations
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
A new method for sensitivity analysis of fuzzy transportation problems
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Fuzzy optimal solution of fully fuzzy linear programming problems using ranking function
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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Linear programming problems with trapezoidal fuzzy variables (FVLP) have recently attracted some interest. Some methods have been developed for solving these problems by introducing and solving certain auxiliary problems. Here, we apply a linear ranking function to order trapezoidal fuzzy numbers. Then, we establish the dual problem of the linear programming problem with trapezoidal fuzzy variables and hence deduce some duality results. In particular, we prove that the auxiliary problem is indeed the dual of the FVLP problem. Having established the dual problem, the results will then follow as natural extensions of duality results for linear programming problems with crisp data. Finally, using the results, we develop a new dual algorithm for solving the FVLP problem directly, making use of the primal simplex tableau. This algorithm will be useful for sensitivity (or post optimality) analysis when using primal simplex tableaus.