The main purpose of this paper is to introduce the concepts of fuzzy T-locality groups. This construct mainly will deal and relate with both fuzzy T-locality spaces (1995) and fuzzy TL-uniform spaces (2006). We establish some basic results and characterization theorems. Also, we show that all
initial and final lifts exist uniquely in the concrete category of fuzzy T-locality groups and hence all initial and final fuzzy T-locality groups exist and can be characterized. As consequences fuzzy T-locality subgroups, fuzzy T-locality product groups and fuzzy T-locality quotient groups are exist.
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