A Vector Similarity Measure for Interval Type-2 Fuzzy Sets

Fuzzy logic is frequently used in computing with words (CWW). When input words to a CWW engine are modeled by interval type-2 fuzzy sets (IT2 FSs), the CWW engine´s output can also be an IT2 FS, A tilde, which needs to be mapped to a linguistic label so that it can be understood. Because each linguistic label is represented by an IT2 FS Bi, there is a need to compare the similarity of A tilde and B tilde_i to find the B tilde_i most similar to A tilde. In this paper, a vector similarity measure (VSM) is proposed for IT2 FSs, whose two elements measure the similarity in shape and proximity, respectively. A comparative study shows that the VSM gives more reasonable results than all other existing similarity measures for IT2 FSs.