A bm Lambda -Cut and Goal-Programming-Based Algorithm for Fuzzy-Linear Multiple-Objective Bilevel Optimization

Ya Gao, Guangquan Zhang, Jun Ma, Jie Lu

Abstract: para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Bilevel-programming techniques are developed to handle decentralized problems with two-level decision makers, which are leaders and followers, who may have more than one objective to achieve. This paper proposes a <formula formulatype="inline"><tex Notation="TeX">${\lambda}$</tex></formula>-cut and goal-programming-based algorithm to solve fuzzy-linear multiple-objective bilevel (FLMOB) decision problems. First, based on the definition of a distance measure between two fuzzy vectors using <formula formulatype="inline"><tex Notation="TeX">${\lambda}$</tex></formula>-cut, a fuzzy-linear bilevel goal (FLBG) model is formatted, and related theorems are proved. Then, using a <formula formulatype="inline"><tex Notation="TeX">${\lambda}$</tex></formula>-cut for fuzzy coefficients and a goal-programming strategy for multiple objectives, a <formula formulatype="inline"><tex Notation="TeX">${\lambda}$</tex></formula>-cut and goal-programming-based algorithm to solve FLMOB decision problems is presented. A case study for a newsboy problem is adopted to illustrate the application and executing procedure of this algorithm. Finally, experiments are carried out to discuss and analyze the performance of this algorithm. </para>