A new method for solving nonlinear complementarity problems in fuzzy environment

Abstract

In this paper, we study a new class of fuzzy nonlinear complementarity problem (FNCP) based on fuzzy sets theory in finite Euclidean spaces. It can be regarded as the extension of classical nonlinear complementarity problem. In order to solve the FNCP, we firstly convert it into a fuzzy mathematical program with equilibrium constraints (FMPEC) by the expected value of fuzzy variables. Furthermore, we construct an auxiliary function, which is used to convert the FMPEC into the reformulation of the problem. Then, we present a new penalty method for solving FNCP. Finally, the rigorous convergence of the penalty method is proved.