A note on Zadeh's extensions

Authors
Roman-Flores, H Barros, LC Bassanezi, RC
Citation
H. Roman-flores et al., A note on Zadeh's extensions, FUZ SET SYS, 117(3), 2001, pp. 327-331
Citations number
12
Categorie Soggetti
Engineering Mathematics
Journal title
FUZZY SETS AND SYSTEMS
ISSN journal
01650114 → ACNP
Volume
117
Issue
3
Year of publication
2001
Pages
327 - 331
Database
ISI
SICI code
0165-0114(20010201)117:3<327:ANOZE>2.0.ZU;2-4
Abstract
Let f: R-n --> R-n and (f) over cap: F(R-n) --> F(R)(n) be Zadeh's extensio n of f to the space of fuzzy compact sets F(R-n). The aim of this paper is to show that if f is continuous, then (f) over cap : (F(R-n), D) --> (F(R-n ), D) is also continuous, D being the supremum over Hausdorff distances bet ween their corresponding level sets. (C) 2001 Elsevier Science B.V. All rig hts reserved.