Multidimensional data in multidimensional scaling using the analytic network process

Multidimensional scaling (MDS) is a statistical tool for constructing a low-dimensional configuration to represent the relationships between the objects. Although MDS has been widely used in various fields, it is difficult to evaluate similarity/ dissimilarity between the complex systems by human judgment. Even though we can divide a complex system into subsystems, which can be more easily evaluated, the relative weights of the subsystems are also a crucial problem. Because of these subsystems usually exist interdependence and feedback, the weights of the subsystems are hard to obtain. This paper proposes a method which combines the methods of the interpretive structural modeling (ISM) and the analytic network process (ANP) procedures to deal with the problem of the subsystems' interdependence and feedback. In addition, we also provide a numerical example to illustrate the proposed method.