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Abstract
The research is based on three stages in the construction process. The first stage is to give new definitions for three different types of Fuzzy sets that we called FI-set, FC-set and SFI-set. The second stage is to use what was defined in the previous stage in order to construct also three new definitions of internal, external and boundary fuzzy sets. Finally, the new concepts and separation axioms were defined using the definitions from the previous two stages.