A Modified Hausdorff Distance Between Fuzzy Sets

Abstract In an earlier paper (B.B. Chaudhuri, A. Rosenfeld, Pattern Recognition Letters 17 (1996) 1157–1160) we defined a Hausdorff-like metric distance between fuzzy sets. This distance contained two terms, one representing geometric distance and the other representing dissimilarity. Combining two terms representing two unrelated notions is not very appealing. In this paper, a modified metric is proposed which contains a single term representing geometric distance only; which reduces to the classical Hausdorff distance when the fuzzy sets are crisp; and which is relatively insensitive to noise.

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