An inclusion measure between general type-2 fuzzy sets

The inclusion measure indicates the degree that a fuzzy set is contained in another fuzzy set and can be used in many fields. However, the inclusion measure between type-2 fuzzy sets has received little attention. Hence in this paper, we propose an inclusion measure for general type-2 fuzzy sets. Firstly, we select an axiomatic definition for the new inclusion measure. Then, according to the selected axiomatic definition, we propose a computation formula by considering the FOU and the secondary membership function of the general type-2 fuzzy set. Finally, we present two examples to explain its calculation and validate its performance. The results show that the proposed inclusion measure is reasonable and reliable for general type-2 fuzzy sets.