Possibilistic Stackelberg solutions to bilevel linear programming problems with fuzzy parameters

This article considers bilevel linear programming problems where the coefficients of the objective functions and the constraints in the problem are given as fuzzy parameters. Stackelberg problems and Stackelberg solutions under fuzziness have not been fully discussed so far. New Stackelberg solution concepts under fuzziness, called possibilistic Stackelberg solutions, are proposed by incorporating possibility theory into Stackelberg solutions in non-fuzzy environments. This paper shows some theoretical properties and theorems on the formulated fuzzy bilevel programming problems. It is shown that the proposed possibilistic Stackelberg solutions are obtained by using linear or nonlinear programming techniques. The effectiveness of the proposed models is demonstrated by numerical experiments using transportation problems where the upper-level decision maker is a buyer and the lower-level one is a supplier.