Natural extensions in fuzzy topology

There exist several approaches to fuzzy neighborhoods and fuzzy neighborhood spaces in fuzzy topology. The paper focuses on M. Ying´s (1994) approach, which is the “fuzziest” among them and by means of which it is possible to define an interesting notion of function continuity. Using a “naturalness” criterion for fuzzy topological constructs introduced here, the paper shows that Ying´s notion of neighborhood is more natural than the others. Additional applications of this criterion are also developed. It is concluded that this naturalness criterion may be useful in comparing and evaluating alternative approaches in fuzzy topology