A Study of Boundedness in Fuzzy Normed Linear Spaces

In the present paper some different types of boundedness in fuzzy normed linear spaces of type (X, N, *), where * is an arbitrary t-norm, are considered. These boundedness concepts are very general and some of them have no correspondent in the classical topological metrizable linear spaces. Properties of such bounded sets are given and we make a comparative study among these types of boundedness. Among them there are various concepts concerning symmetrical properties of the studied objects arisen from the classical setting appropriate for this journal topics. We establish the implications between them and illustrate by examples that these concepts are not similar.