From Fuzzy Universal Approximation to Fuzzy Universal Representation: It All Depends on the Continuum Hypothesis

Authors

Mahdokhat Michelle Afravi, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

5-2017

Comments

Technical Report: UTEP-CS-17-25b

To appear in Proceedings of the Joint 17th Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems, Otsu, Japan, June 27-30, 2017.

Abstract

It is known that fuzzy systems have a universal approximation property. A natural question is: can this property be extended to a universal representation property? Somewhat surprisingly, the answer to this question depends on whether the following Continuum Hypothesis: every infinite subset of the real line has either the same number of elements as the real line itself or as many elements as natural numbers.