On Hausdorff-like metrics for fuzzy sets
نویسنده
چکیده
In (Chaudhuri and Rosenfeld, 1996), metrics were developed for fuzzy sets u and v defined on the same support set S. These metrics are based on applying the Hausdorff metric to pairs of membership level sets (u 1 ( [ tk, 1 ] ), v1 ( [ tk, 1 ] ) ), where tk E [0, 1] is a (possible) membership value of u or v. The metrics of (Chaudhuri and Rosenfeld, 1996) give nice comparisons of fuzzy sets by measuring the differences in their images, but suffer the undesirable restriction that fuzzy sets so compared must have the same maximum values. In the current paper, we show how the metrics of (Chaudhuri and Rosenfeld, 1996) may be modified so as to remove this restriction while preserving some of the "feel" of the metrics described in (Chaudhuri and Rosenfeld, 1996). We also present an algorithm for computing our metric that runs in O(mn) time for a 2-dimensional digital picture of n pixels on which fuzzy sets are allowed m distinct membership values. © 1997 Elsevier Science B.V.
منابع مشابه
Corrigenda to "On Hausdorff-like metrics for fuzzy sets" [Pattern Recognition Lettes Vol. 18, (1997) 115-118]
Our paper was motivated by (Chaudhuri and Rosenfeld, 1996), a paper in which several metrics related to the Hausdorff metric are given for fuzzy sets defined on the same nonempty support set S. The first metric given in (Chaudhuri and Rosenfeld, 1996), denoted F 0 in our paper, requires all the fuzzy sets considered by F 0 to have the same maximum value. Chaudhuri and Rosenfeld (1996) then modi...
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ورودعنوان ژورنال:
- Pattern Recognition Letters
دوره 18 شماره
صفحات -
تاریخ انتشار 1997