The purpose of this book is to introduce some new definitions of separation axioms in supra fuzzy topological spaces using the ideas of Ali 8]. Some of their equivalent formulations along with various new characterizations and results concerning the existing ones are presented here. Our criterion for definitions has been preserving as much as possible the relation between the corresponding separation properties for supra fuzzy topological spaces. Moreover, it will be seen that the definitions of these axioms are 'good extensions' in the sense of Lowen 60]. We aim to develop theories of supra fuzzy T0, supra fuzzy T1, supra fuzzy T2(Hausdorff), supra fuzzy SFR(supra fuzzy regular), supra fuzzy SFN(supra fuzzy normal), supra fuzzy R0- and supra fuzzy R1- separation axioms analogous to its counter part in ordinary topology. We also prove that all the concepts are hereditary, productive and projective.

The purpose of this book is to sujjest new definitions of separation axioms in fuzzy bitopological spaces. We study several features of these definitions along with the existing ones. The introduce concepts are less restrictive than those of Kandil and El-Shafee 66,67] as will be found later on. Our criteria for definitions have been preserved as much as possible the relation between the corresponding separation properties for fuzzy topological space. Moreover, it will be seen that the definitions of these axioms are "good extensions" in the sence of 92] due to Lowen. All the definitions are added here, we established the relation among them also, we find the relation among general topology, general bitopology, fuzzy topology and fuzzy bitopology. In this book, we show that all of these definitions satisfy the property of Hereditary, Productive and Projective.