Enhanced Interval Approach for encoding words into interval type-2 fuzzy sets and convergence of the word FOUs

The Interval Approach (IA) [4] is a method for synthesizing an interval type-2 fuzzy set (IT2 FS) model for a word from data that are collected from a group of subjects. A key assumption made by the IA is: each person's data interval is random and uniformly distributed. This means, of course, that the IT2 FS model for the word is random. Consequently, one can question whether or not the IT2 FS model for the word converges in a stochastic sense. This paper focuses on this question. As a part of our study, we have had to modify some steps of the IA, the resulting being an Enhanced IA (EIA). The paper shows by means of some simulations, that the IT2 FS word models that are obtained from the EIA are converging in a mean-square sense. This provides substantial credence for using the EIA to obtain T2 FS word models.