The suprem metric D between fuzzy subsets of a metric space is the supremum of the Hausdorff distances of the corrisponding level sets. In this papier some new criteria of compactness with respect to the distance D are given; they concern arbitrary fuzzy sets, fuzzy sets having no proper local maximum points end, finally, fuzzy sets with convex sendograph. In order to compare results with a previous characterization of compactness of Diamond-Kloeden, the criteria will be expressed by equi-( left-right)-continuity.
Supremum metric and relatively compact sets of fuzzy sets
Greco, Gabriele Hans;Moschen, Maria Pia
2006-01-01
Abstract
The suprem metric D between fuzzy subsets of a metric space is the supremum of the Hausdorff distances of the corrisponding level sets. In this papier some new criteria of compactness with respect to the distance D are given; they concern arbitrary fuzzy sets, fuzzy sets having no proper local maximum points end, finally, fuzzy sets with convex sendograph. In order to compare results with a previous characterization of compactness of Diamond-Kloeden, the criteria will be expressed by equi-( left-right)-continuity.File in questo prodotto:
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