Visual Analysis and Representations of Type-2 Fuzzy Membership Functions

This paper presents several pictorial and graphical techniques that may be used for effectively visualizing type-2 fuzzy membership functions (T2 FMFs). In our first proposed technique, two-dimensional data sets have been modeled using grayscale entropies to make the uncertainty interpretation easier. Next, the concept of a vertical drill and a primary membership drill has been introduced to obtain information from a T2 FMF representing a multi-dimensional data set. Further, the generation of general T2 FMFs with secondary membership functions in the form of asymmetric Gaussian distributions, referred to as "snaky" surfaces, has been discussed as an extension of symmetric Gaussian T2 FMF. These graphical techniques may be applied for making inferences or predictions about the uncertainty level of a T2 FMF in applications such as data clustering, computing with words (CWW), and logic control for robots, to name a few.