The similarity and inclusion measures between fuzzy sets are two important concepts in fuzzy set theory, but little
effort as to them has been made on type-2 fuzzy sets. Therefore, a similarity measure and an inclusion measure between
interval type-2 fuzzy sets (IT2 FSs) are proposed. Firstly, the axiomatic definitions of two measures are selected. Then, based
on the selected definitions, the computation formulas are proposed, and four theorems that two measures can be transformed
by each other are demonstrated. Finally, examples are presented to validate their performance and combine the proposed
similarity measure with Yang and Shih’s clustering method for an application to clustering analysis of Gaussian IT2 FSs, and
a reasonably hierarchical clustering tree in different ??-levels is obtained. Simulation results show the practicability of the
proposed measures.