The fuzzy neural network approximation lemma

✍ Scribed by Thomas Feuring; Wolfram-M. Lippe

• Book ID: 104292470
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 732 KB
• Volume: 102
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(97)00125-5

✦ Synopsis

It is well known that artificial neural networks are universal approximators. But what about fuzzy neural networks? Only Buckl, ey and Hayashi [1] presented a theoretical result for these networks: They showed that there are fuzzy functions which cannot be approximated by a certain fuzzy neural network. In this paper we answer the question for a special type of fuzzy neural networks -especially with regard to the fuzzy arithmetic that is used: It is simplified in order to minimize the computational expense as well as to simplify the theoretical examinations. We prove that the class of fuzzy functions which is identical to the class of all continuous real functions extended by means of the extension principle can be approximated by certain fuzzy neural networks.