Neurofuzzy Cognitive Maps with Adaptive B-splines

Abstract

Cognitive maps and time space maps make use of multidimensional scaling (MDS) techniques to analyze data relating to spatial and environmental preferences and perception. Perceptual configuration of the points is represented by a cognitive map with surface feature interpolation. In this paper we propose a procedure of MDS using Neurofuzzy adaptive modelling with B-splines for surface feature interpolation. The procedure is compared with those using Hayashi's quantifying method of paired comparisons and Torgerson's metrical multidimensional scaling procedure. In numerical examples, the resultant maps are compared and an application to sociometry analysis is presented. It is shown that by introducing a simple term to the objective function the topological distortion can be drastically improved.