Which Truth Values in Fuzzy Logics are Definable?

Authors

Hung T. Nguyen
Vladik Kreinovich, The University of Texas at El PasoFollow
Antonio Di Nola

Publication Date

4-2001

Comments

UTEP-CS-01-10a.

Short version published in: Proceedings of the NEW New Paradigms for the New Millennium Conference, Caserta, Italy, September 13-15, 2001; full paper published in International Journal of Intelligent Systems, 2003, Vol. 18, No. 10, pp. 1057-1064.

Abstract

In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval [0,1]. There are only denumerable many words and phrases, and continuum many real numbers; thus, not every real number corresponds to some commonsense degree of uncertainty. In this paper, for several fuzzy logic, we describe which numbers are describing such degrees, i.e., in mathematical terms, which real numbers are definable in the corresponding fuzzy logic.