05.04.2016 | Methodologies and Application | Ausgabe 18/2017
An approach for solving a fuzzy bilevel programming problem through nearest interval approximation approach and KKT optimality conditions
- Zeitschrift:
- Soft Computing > Ausgabe 18/2017
Wichtige Hinweise
Communicated by V. Loia.
Abstract
In this paper, we consider a kind of bilevel linear programming problem where the coefficients of both objective functions are fuzzy numbers. In order to deal with such a problem, the original problem can be approximated by an interval bilevel programming problem in terms of the nearest interval approximation of a fuzzy number. Based on the Karush–Kuhn–Tucker (KKT) optimality conditions for the optimization problem with an interval-valued objective function, the interval bilevel programming problem can be converted into a single-level programming problem with an interval-value objective function. To minimize the interval objective function, the order relations of interval numbers are used to transform the uncertain single-objective optimization into a multi-objective optimization solved by global criteria method (GCM). Finally, illustrative numerical examples are provided to demonstrate the feasibility of the proposed approach.
