Philosophical Interpretation of Connection of Robust Statistics and Fuzzy Logic: The Robust Fuzzy Clustering

Abstract

Clustering methods have the key role in pattern recognition, computer vision, and control. In real applications, the data are corrupted with stochastic noise which often has outliers. It follows that clustering techniques need to be robust. It is observed that robust statistics and fuzzy set theory have much in common. Namely, the concept of weight functions in robust statistics can be related to the concept of membership function in fuzzy set theory. In the paper proposed the new objective function for cluster analysis. For the clustering the modified Gustafson-Kessel algorithm is used and the modification is based on possibility theory. The final goal is membership function determination. That is the important part of the Takagi–Sugeno models which represent the fuzzy model of nonlinear dynamic systems.