A Vector Similarity Measure for Type-1 Fuzzy Sets

摘要

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 A with 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 A and 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.