Abstract
The aim of this work is to construct a new structure which is called fuzzy group bornology to solve the problem of bounded for fuzzy group. Furthermore, we explain that the intersection of collections of fuzzy bornological groups is a fuzzy bornological group. Also, we gave the sufficient condition to show the image of a fuzzy bornological group is fuzzy bornological group and showed there exist a fuzzy bornological isomorphism between two fuzzy bornological groups. Finally, we studied a homomorphism between fuzzy bornological groups with some main properties and some results and show that a fuzzy bornological group is homogenous space.
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