A Vector Similarity Measure for Type-1 Fuzzy Sets

Authors:
Dongrui Wu;Jerry M. Mendel
Affiliations:
Signal and Image Processing Institute, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089-2564,;Signal and Image Processing Institute, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089-2564,
Venue:
IFSA '07 Proceedings of the 12th international Fuzzy Systems Association world congress on Foundations of Fuzzy Logic and Soft Computing
Year:
2007

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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 Awith a linguistic label from a vocabulary. Because each label is represented by an T1 FS Bi, there is a need to compare the similarity of Aand Bito find the Bimost 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.