Bi-directional nearness in a network by AHP (Analytic Hierarchy Process) and ANP (Analytic Network Process)

In this paper we study bi-directional nearness in a network based on AHP (A nalytic Hierarchy Process) and ANP (Analytic Network Process). Usually we u se forward (one-dimensional) direction nearness based on Euclidean distance . Even if the nearest point to i is point j, the nearest point to j is not necessarily point i. So we propose the concept of bi-directional nearness d efined by AHP's synthesizing of weights "for" direction and "from" directio n. This concept of distance is a relative distance based on the configurati on of the set of points located on a plane or network. In order to confirm the usefulness of our study we apply the proposed nearness to solving metho ds of TSP (Traveling Salesman Problem), where to find an approximate soluti on of TSP we improved Nearest Neighbor Method. Some numerical experiments o f TSP were carried out. To decide a nearest point we used two kind of nearn ess, forward direction nearness and bi-directional nearness. As a result, b y using bi-directional nearness, we obtained good approximate solution of T SP. Moreover, the relation between AHP and ANP, through an example, is cons idered.