GENERALIZED FUZZY METRIC SPACES

The theory of generalized metric spaces is closely related to what is known as ¿metrization theory''. They can be used to characterize the images or pre images of metric spaces under certain kinds of mappings. They have appeared as a ¿factor'' in many metrization theorems. The fuzzy analogues of these spaces are more significant. The class of generalized fuzzy metric spaces like fuzzy M-spaces, fuzzy w¿-Spaces and fuzzy Moore space are introduced in this book. We prove how these spaces are related to fuzzy metrizable spaces and some vital properties of these spaces are proved. The concept of a fuzzy network is one of the useful tools in the theory of generalized fuzzy metric spaces. The fuzzy ¿- spaces is a class of generalized metric space having an ¿ ¿ discrete fuzzy network. The class of p- spaces generalizes both metrizable spaces and compact spaces. Hence concept of fuzzy p- spaces is more important. The nice relationships between various generalized fuzzy metric spaces like, fuzzy Moore spaces, fuzzy ¿-spaces, fuzzy w¿-spaces, fuzzy p- spaces and how they are connected to fuzzy metric spaces are investigated.