Stability of multi-objective bi-level linear programming problems under fuzziness

Abstract

This paper deals with multi-objective bi-level linear programming problems under fuzzy environment. In the proposed method, tentative solutions are obtained and evaluated by using the partial information on preference of the decision-makers at each level. The existing results concerning the qualitative analysis of some basic notions in parametric linear programming problems are reformulated to study the stability of multi-objective bi-level linear programming problems. An algorithm for obtaining any subset of the parametric space, which has the same corresponding Pareto optimal solution, is presented. Also, this paper established the model for the supply-demand interaction in the age of electronic commerce (EC). First of all, the study uses the individual objectives of both parties as the foundation of the supply-demand interaction. Subsequently, it divides the interaction, in the age of electronic commerce, into the following two classifications: (i) Market transactions, with the primary focus on the supply demand relationship in the marketplace; and (ii) Information service, with the primary focus on the provider and the user of information service. By applying the bi-level programming technique of interaction process, the study will develop an analytical process to explain how supply-demand interaction achieves a compromise or why the process fails. Finally, a numerical example of information service is provided for the sake of illustration.

Keywords

• multi-objective bi-level linear programming problems
• partial information of preference
• stability