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On links between mathematical morphology and rough sets

✍ Scribed by Isabelle Bloch

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
129 KB
Volume
33
Category
Article
ISSN
0031-3203

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✦ Synopsis

Based on the observation that rough sets and mathematical morphology are both using dual operators sharing similar properties, we investigate more closely the links existing between both the domains. We establish the equivalence between some morphological operators and rough sets de"ned from either a relation, or a pair of dual operators or a neighborhood system. Then we suggest some extensions using morphological thinning and thickening, and using algebraic operators. We propose to de"ne rough functions and fuzzy rough sets using mathematical morphology on functions and fuzzy mathematical morphology.

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Although fuzzy operators have deserved a large attention in the Euclidean case, almost nothing exists concerning the geodesic case. In this paper, we address this question, by de"ning fuzzy geodesic distances between points in a fuzzy set, and geodesic balls in a fuzzy set (based on the comparison o