On the relationship between the centroid and the footprint of uncertainty of Interval Type-2 fuzzy numbers

This paper presents experimental results about the relationship between the Footprint Of Uncertainty (FOU) and the centroid of Interval Type-2 Fuzzy Numbers (IT2FN) which are a subclass of Type-2 fuzzy numbers. Four types of IT2FNs are analyzed: singleton-core triangular, interval-core triangular, singleton-core Gaussian and interval-core Gaussian IT2FNs. A quadratic relationship was detected, characterized, and their results are presented and discussed using numerical experiments.