The paper aims to develop a framework for coalgebraic fuzzy geometric logic
by adding modalities to the language of fuzzy geometric logic. Using the
methods of coalgebra, the modal operators are introduced in the language of
fuzzy geometric logic. To define the modal operators, we introduce a notion of
fuzzy-open predicate lifting. Based on coalgebras for an endofunctor T on the
category Fuzzy-Top of fuzzy topological spaces and fuzzy continuous
maps, we build models for the coalgebraic fuzzy geometric logic. Bisimulations
for the defined models are discussed in this work