Abstract
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.
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Wu, D., Mendel, J.M. (2007). A Vector Similarity Measure for Type-1 Fuzzy Sets. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_57
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DOI: https://doi.org/10.1007/978-3-540-72950-1_57
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