Simultaneous solution of a fuzzy global optimization problem using a fixed point method

Abstract

In this paper, we adopt a fixed point approach towards a problem of finding fuzzy distance between two subsets of a fuzzy metric space. This is accomplished simultaneously by determining two different pairs of points which are obtained by finding an optimal approximate solution of a coupled fixed point equation for an appropriate coupled contractive operator. By its nature, the problem is a global optimization problem. The coupled contraction defined here has certain properties suitable for applications to the optimization problem considered in this paper. The main result is illustrated with an example. By applications of the main theorem, a new coupled fixed point result is derived in fuzzy metric space and a new coupled proximity point result is obtained in metric spaces. This work is a continuation of a newly emerged line of research on global optimization in the context of fuzzy metric spaces.