Abstract
The concept of fuzzy space is introduced. This concept corresponds to the concept of the universal set in the ordinary case. The algebra of fuzzy spaces and fuzzy subspaces is studied. Using the concept of fuzzy space and fuzzy binary operation, a new approach to study fuzzy group theory is given. This approach can be considered as a generalization and reformulation of the Rosenfeld theory of fuzzy subgroups. Therefore, it is an active tool to develop the theory of fuzzy groups.
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