The stability notions for fuzzy nonlinear programming problem

This paper deals with the stability of fuzzy multiobjective nonlinear programming (FMONLP) problem. The stability and the stability notions of parametric nonlinear programming problem are extended to redefine and analyze the stability and stability notions of FMONLP. The concept of alpha-fuzzy efficient was introduced in which the ordinary efficient solution is extended based on the alpha-cut of fuzzy numbers. A necessary and sufficient condition for such a solution is established. The basic notions of stability (the solvability set and the stability set of the first kind) are redefined and analyzed qualitatively and quantitatively for the problem. An example is given for the sake of illustration.