Interactive stability of vector optimization problems

Abstract This paper presents a solution method for multiobjective nonlinear programming (MONLP) problems and the stability of this solution. The method, called interactive stability compromise programming (ISCP), offers a practical solution to MONLP problems by deriving the compromise weights and combining judgement with an automatic optimization technique in fuzzy decision making. This is achieved by using the method of compromise programming and the method of compromise weights and we obtain the stability for the solution in each step of the algorithm. A numerical example illustrates various aspects of the results developed in this paper.