On the convergence of fuzzy-number-valued functions

✍ Scribed by Byung Moon Ghil

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 163 KB
• Volume: 87
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(96)00034-6

✦ Synopsis

We show that given a sequence {f,} of uniformly continuous real-valued functions which converges uniformly on a separable Banach space E, the sequence {F,} of fuzzy-number-valued functions on X, induced by f, through Zadeh's extension, converges uniformly with respect to the Hausdorff metrics on Fc~(E) and F~¢(R), Also we show by example that if {f,} converges pointwise then the corresponding {F,} does not converge in general. (~)