A Vector Similarity Measure for Type-1 Fuzzy Sets

Comparing the similarity between two fuzzy sets (FSs) is needed in many applications. The focus herein is linguistic approximation using type-1 (T1) FSs, i.e. associating a T1 FS Awith a linguistic label from a vocabulary. Because each label is represented by an T1 FS B i , there is a need to compare the similarity of Aand B i to find the B i most similar to A. In this paper, a vector similarity measure (VSM) is proposed for T1 FSs, whose two elements measure the similarity in shape and proximity, respectively. A comparative study shows that the VSM gives best results. Additionally, the VSM can be easily extended to interval type-2 FSs.