Obtaining an FOU for a word from a single subject by an individual interval approach

Recently a simple and practical type-2-fuzzistics methodology called an interval approach (IA) was presented for obtaining interval type-2 fuzzy set (IT2 FS) models for words using data collected from a group of subjects. There may be times, however, when a group of subjects is not available. This paper proposes a way to obtain IT2 FS models from words collected from a single subject using an IA, and is called an individual IA (IIA). Two methods are presented for doing this. Both use end-point and uncertainty data that are collected from an individual, assume a probability distribution on each interval, map them into pre-specified T1 membership functions (MF), interpret the MFs as nine embedded T1 FSs of an IT2 FS, and then aggregate the FSs using union to obtain the footprint of uncertainty (FOU) for the word. This approach not only captures the strong points of the previously developed IA but simplifies it. Experiments show that the IIA is easy to implement and the resulting FOUs match our intuition.