Similarity and nearness of fuzzy sets
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TL;DR
This work constructs some new similarity measure by the optimum factor of proportionality with l/sup 2/-norm, which is proposed by Kosko or Wang and is based on the mutual subsethood theorem.
Abstract
Similarity measure of fuzzy sets can boils down to distance nearness and "shape" similarity of two fuzzy sets, and distance nearness of two fuzzy sets can be regarded the question of least value of some function with some norm, and similarity measure can be defined the optimum factor of proportionality. Mutual subsethood theorem proposed by Kosko or Wang is the optimum factor of proportionality with l/sup 1/-norm. We construct some new similarity measure by the optimum factor of proportionality with l/sup 2/-norm.