A Proposal of Fuzzy Modeling on Fusion Axes

Abstract

Transparency of fuzzy models has become one of the major topics in the field of fuzzy modeling. This paper discusses a methodology for constructing transparent models that have clear input-output relationships of unknown systems. Visualization of data in two/three dimensions is one of effective methods for obtaining the transparency. This paper proposes a visualization method of input-output relationships with a new dimensionality reduction method. This paper also presents a method that constructs fuzzy models in the visualized space for knowledge extraction. The proposed method is to obtain transparent models for understanding input-output relationships of unknown systems, and thus to show guidelines for constructing models with more appropriate structures. This paper defines "fusion axes" that are linear transformation of input variables for dimensionality reduction. The proposed method constructs a transparent model on the fusion axes using Fuzzy C-Means and Fuzzy Multiple Discriminant Analysis. This paper shows thorough a numerical experiment that the proposed method can identify an appropriate fusion axis to visualize the input-output relationships. This paper also applies the proposed method to gas furnaces data. This experiment shows that the proposed method finds a proper model structure by visualizing the input-output relationships.