Bi-Level Linear Programming Model and Algorithm with Trapezoidal Fuzzy Numbers for a Class of Variable
Fuzzy bi-level linear programming is a combination of fuzzy mathematics and bi-level linear programming studying a bi-level linear programming model with trapezoidal fuzzy numbers.According to the fuzzy structured element theory,there is an one-to-one correspondence relationship between bounded real fuzzy numbers and standard monotonic bounded function in[-1,1],getting the conclusion that the order between fuzzy numbers can be converted to the order between monotonic functions,then defining the structured element's weighted order of fuzzy numbers,and proving that the optimal solution of an bi-level linear programming problem with trapezoidal fuzzy numbers is equivalent to the optimal solution of an bi-level linear programming problem.On the premise of bi-level linear programming's constrained set is nonempty and bounded,the feasible set is both a weak quasi-convex set and connected set,then getting the most optimistic condition of BLP problem by duality theory,then transforming the bi-level linear programming problem to linear programming problem,finally solve the linear programming problem by MATLAB programming.
fuzzy structured elementtrapezoidal fuzzy numbersbi-level linear programming
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