Stability of multiciteria nonlinear programming problems using fuzziness

Abstract

This paper presents a generalized fuzzy approach for determining the stability of multicriteria nonlinear programming problems. The proposed approach refers to an ideal, equivalent, single objective representation for the whole objectives. The membership functions for each objective function are constructed and, by the proposed formulation, the multicriteria programming problem will be transformed to an ideal equivalent single problem. By the proposed approach, the crisp intervals for the stability could be determined for the multicriteria nonlinear programming problems after solving two single nonlinear problems. Two illustrative examples are presented to verify the idea of the proposed stability approach. © 2002 Elsevier Science B.V. All rights reserved.