FUZZY RESOLUTION ON THE INFEASIBILITY OF VARIATIONAL INEQUALITY

In this study, we discuss variational inequality problems when there i s no solution. By applying fuzzy set theory, we ''soften'' the origina l problem with fuzzy relation and denote it by (VI) over tilde(X,f). T hen the solutions which satisfy the variation inequality to some degre e mu,0 less than or equal to mu 1 are searched with minimum relaxation . According to the proposed existence theorem, an approach derived fro m the concepts of single objective mathematical programming problems f or solving the (VI) over tilde(X,f) is proposed to find its fuzzy solu tion set. (C) 1998 Elsevier Science Inc. All rights reserved.