Type-2 Fuzzy C-Means Incorporating Locality Sensitive Space Information

This paper presents a new extensions of fuzzy c-means (FCM) incorporating locality sensitive space information based on type-2 fuzzy sets referred to as T2LFCM. The estimated kernel widths of fuzzy c-means incorporating locality sensitive space information(LFCM) may not accurately reflect the underlying distributions of the observations because of insufficient and noisy data in real-world problems. To handle the uncertainties and lessen the sensitivity of the parameters existing in real problems, we apply interval type-2 fuzzy sets to construct T2LFCM. By three-dimensional membership functions of type-2 fuzzy sets, T2LFCM uses footprint of uncertainty (FOU) as well as interval secondary membership functions to handle LFCM uncertain kernel width, and thus T2LFCM parameters vary anywhere in an interval with uniform possibilities. As a result, every kernel width becomes a interval rather than a precise real number to account for LFCM uncertainty. These intervals are then processed by the expectation maximization (EM) algorithm and probability theory. Experiments on liver image demonstrate the effectiveness of the proposed T2LFCM.