An adaptive type-2 input based nonsingleton type-2 Fuzzy Logic System for real world applications

A Fuzzy Logic System (FLS) is generally credited with being an adequate methodology for real world applications which are subject to high uncertainty levels. Recent works have shown that interval type-2 FLSs can outperform type-1 FLSs in the applications which encompass high uncertainty levels. However, the majority of interval type-2 FLSs handle the linguistic and input numerical uncertainties using singleton interval type-2 FLSs that mix the numerical and linguistic uncertainties to be handled only by the linguistic labels type-2 fuzzy sets. This ignores the fact that if input numerical uncertainties were present, they should affect the incoming inputs to the FLS. Even in the papers that employed nonsingleton type-2 FLSs, the input signals were assumed to have a predefined shape (mostly Gaussian or triangular) which might not reflect the real uncertainty distribution which can vary with the associated measurement. In our previous work, we have presented some of the theoretical basis for generating an adaptive type-2 fuzzy input which is better able to represent the encountered uncertainty at a given measurement. The nonsingleton type-2 fuzzy inputs are dynamic and they are automatically generated from data and they do not assume a specific shape about the uncertainty distribution associated with the given sensor. In this paper, we will present an overview on how the adaptive type-2 input based nonsingleton interval type-2 FLS can operate in real time. We will present real world experiments using a mobile robot which will show how under high input uncertainty levels, the nonsingleton type-2 FLS can give a good performance and outperform its singleton type-2 and type-1 FLSs counterparts.