Two Algorithms For Solving Fuzzy Bilevel Linear Programming Problem

The thesis proposes a fuzzy penalty function algorithm and a Kth-best solution algorithm for solving bilevel linear programming problem with trapezoidal fuzzy variables(FBLP).This paper focuses on a special kind of FBLP,in which the right-hand sides of the upper and lower level constraint functions are trapezoidal fuzzy variables,and obtaining its fuzzy solution by directly using the fuzzy penalty function algorithm and the Kth-best algorithm.The fuzzy penalty function algorithm's main idea is about transforming the FBLP into a single level fuzzy programming problem and then solving it with fuzzy simplex mothed.Firstly,FBLP replaces the lower level problem with setting its duality gap equal to zero and adds duality gap to the objective function as the penalty term.Then the fuzzy penalty function algorithm solves the single level problem with fuzzy simplex mothed.The Kth-best algorithm establishes the definition of the basic feasible solution and creates specific search method to find the fuzzy optimization solution.With the given definition and creative method,we fulfill the Kth-best solution algorithm for FBLP.After proving the feasibility of fuzzy penalty function algorithm and Kth-best solution algorithm,we present the detailed steps of this algorithm.Two numerical examples with detailed results show that both algorithm can solve FBLP well.