Title :
The cardinality of the set of all fuzzy numbers
Author :
Zhenyuan Wang ; Zhang-Westman, Li
Author_Institution :
Dept. of Math., Univ. of Nebraska at Omaha, Omaha, NE, USA
Abstract :
The concept of fuzzy numbers is a generalization of the concept of real numbers. Intuitively, there are more fuzzy numbers than real numbers, that is, the cardinality of the set consisting of all fuzzy numbers should not be smaller than the cardinality of the set of all real numbers. In this work, based on a newly established Decomposition Theorem IV for fuzzy sets, a one-to-one mapping from the set of all fuzzy numbers into interval (0, 1] can be established. This means that the cardinality of the set of all fuzzy numbers is the same as the cardinality of interval (0, 1]. The discussion in this paper is significant to ranking and ordering fuzzy numbers.
Keywords :
fuzzy set theory; decomposition theorem IV; fuzzy numbers concept; fuzzy set theory; one-to-one mapping; real numbers concept; Educational institutions; Fuzzy sets; Kernel; Nickel; Noise measurement; Vectors; Fuzzy sets; cardinal numbers; cardinality of sets; decomposition theorem; fuzzy numbers;
Conference_Titel :
IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013 Joint
Conference_Location :
Edmonton, AB
DOI :
10.1109/IFSA-NAFIPS.2013.6608544
