General Type-2 Fuzzy C-Means Algorithm for Uncertain Fuzzy Clustering

Pattern recognition in real-world data is subject to various sources of uncertainty that should be appropriately managed. The focus of this paper is the management of uncertainty associated with parameters of fuzzy clustering algorithms. Type-2 fuzzy sets (T2 FSs) have received increased research interest over the past decade, primarily due to their potential to model various uncertainties. However, because of the computational intensity of the processing of general T2 fuzzy sets (GT2 FSs), only their constrained version, i.e., the interval T2 (IT2) FSs, were typically used. Fortunately, the recently introduced concepts of α-planes and zSlices allow for efficient representation and computation with GT2 FSs. Following this recent development, this paper presents a novel approach for uncertain fuzzy clustering using the general type-2 fuzzy C-means (GT2 FCM) algorithm. The proposed method builds on top of the previously published IT2 FCM algorithm, which is extended via the α- planes representation theorem. The fuzzifier parameter of the FCM algorithm can be expressed using linguistic terms such as “small” or “high,” which are modeled as T1 FSs. This linguistic fuzzifier value is then used to construct the GT2 FCM cluster membership functions. The linguistic uncertainty is transformed into uncertain fuzzy positions of the extracted clusters. The GT2 FCM algorithm was found to balance the performance of T1 FCM algorithms in various uncertain pattern recognition tasks and to provide increased robustness in situations where noisy or insufficient training data are present.

I. Introduction

Pattern recognition algorithms are commonly subject to various sources of uncertainty that should be appropriately managed. Several forms of uncertainties are typically recognized. for instance, the uncertainty related to the input data themselves (e.g., clustering heterogeneous input data such as real numbers, intervals, and linguistic terms), the uncertainty related to the interpretation of the computed result, and the uncertainty related to the suitable parameters' values of the pattern recognition algorithms. The scope of this paper is the appropriate uncertainty management for fuzzy clustering algorithms [1]–[4].