New subsethood measures and similarity measures of fuzzy sets

In this paper, two existing subsethood measures are reviewed at first. An example is given to show that they are not coincident with the l/sup p/-distance in describing the degree of similarity between fuzzy sets. To overcome the flaw, we propose two new subsethood measures, and induce two new similarity measures. Some examples are given to compare and analyze their performance. In addition, it is found that they have equivalent fuzzy entropy with Kosko and Wang's methods respectively.