Title :
Natural topology via fuzzy metric
Author :
Santana, Fagner ; Santiago, Regivan
Author_Institution :
Dept. of Math., UFRN, Natal, Brazil
Abstract :
In this paper, we propose a natural way to define topologies by using fuzzy metrics; here the value of the distance between two points is a non-negative fuzzy number. With such topology, we also define notions like continuity, convergent sequence, Cauchy sequences and complete spaces. As an application, we provide a fixed point theorem quite similar to the classical Banach´s theorem.
Keywords :
fuzzy set theory; topology; Banach theorem; Cauchy sequences; convergent sequence; fuzzy metric; natural topology; nonnegative fuzzy number; Bridges; Cost accounting; Electronic mail; Extraterrestrial measurements; Topology; α-cuts; Fuzzy metric; continuity; fixed point; fuzzy numbers; intervals; topology;
Conference_Titel :
Fuzzy Systems (FUZZ), 2011 IEEE International Conference on
Conference_Location :
Taipei
Print_ISBN :
978-1-4244-7315-1
Electronic_ISBN :
1098-7584
DOI :
10.1109/FUZZY.2011.6007348