کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
844760 | 908612 | 2006 | 11 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Supremum metric and relatively compact sets of fuzzy sets Supremum metric and relatively compact sets of fuzzy sets](/preview/png/844760.png)
The supremum metric D between fuzzy subsets of a metric space is the supremum of the Hausdorff distances of the corresponding level sets. In this paper some new criteria of compactness with respect to the distance D are given; they concern arbitrary fuzzy sets (see Theorem 7), fuzzy sets having no proper local maximum points (see Theorem 12) and, finally, fuzzy sets with convex sendograph (see Theorem 13). In order to compare results with a previous characterization of compactness of Diamond–Kloeden, the criteria will be expressed by equi-(left/right)-continuity. In the proofs a first author's purely topological criterion of D -compactness and a variational convergence (called ΓΓ-convergence) which was introduced by De Giorgi and Franzoni, are fundamental.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 64, Issue 6, 15 March 2006, Pages 1325–1335