  The major part of this thesis deals with fuzzy geometric logic and fuzzy
geometric logic with graded consequence. The first chapter mainly contains the
concept of topological system introduced by S. Vickers in 1989. In Chapter 2
the notion of fuzzy topological system is introduced and categorical
relationship with fuzzy topology and frame is discussed in detail. Also this
chapter contains some methodology to make new fuzzy topological systems from
the old one.Chapter 3 provides a generalization of fuzzy topological system
which shall be called L topological system and categorical relationships with
appropriate topological space and frame. Furthermore, two ways of constructing
subspaces and subsystems of an L topological space and an L topological system
are respectively provided.Chapter 4 deals with the concept of variable basis
fuzzy topological space on fuzzy sets and contains a new notion of variable
basis fuzzy topological systems whose underlying sets are fuzzy sets. In this
chapter categorical relationship between space and system is established.
Chapter 5 contains a different proof of one kind of generalized stone duality,
which was done directly by Maruyama, introducing a notion of n fuzzy Boolean
system. The last two chapters, Chapter 6 and Chapter 7 deal the ultimate
objective. Chapter 6 deals with the question- From which logic fuzzy topology
can be studied?. To answer this, the notion of fuzzy geometric logic is
invented.
