Visualization of two-dimensional interval type-2 fuzzy membership functions using general type-2 fuzzy membership functions

In this paper, we propose a novel method for visualizing two-dimensional interval type-2 fuzzy membership functions (2-D IT2 FMFs) using one-dimensional general type-2 fuzzy membership functions (1-D GT2 FMFs), and also describe the procedure for extending our method to fuzzy sets representing higher dimensional data. Then we present a type reduction method for mapping 2-D IT2 fuzzy sets into 2-D type-1 fuzzy sets that uses alpha-plane representation of general fuzzy sets. We discuss the problem of “multiple membership values for the same element,” which violates set properties, in an IT2 Fuzzy C-means (FCM) algorithm for clustering and propose a solution that uses transformations in the visualization method. These techniques can be applied to applications involving fuzzy sets that represent multidimensional data for proper visualization and type reduction, such as image segmentation, classification and prediction, to name a few.