A modified Hausdorff distance between fuzzy sets

In an earlier paper (B.B. Chaudhuri, A. Rosenfeld, Pattern Recognition Lett ers 17 (1996) 1157-1160) we defined a Hausdorff-like metric distance betwee n fuzzy sets. This distance contained two terms, one representing geometric distance and the other representing dissimilarity. Combining two terms rep resenting two unrelated notions is not very appealing. In this paper, a mod ified metric is proposed which contains a single term representing geometri c distance only; which reduces to the classical Hausdorff distance when the fuzzy sets are crisp; and which is relatively insensitive to noise. (C) 19 99 Elsevier Science Inc. All rights reserved.