Abstract Based on earlier papers by the author [4, 5] finitely generated T-fuzzy linear spaces, T being a general t-norm, are introduced and studied. First, a few basic definitions and notations are presented for reference purposes. Next, in Section 3, a definition of finitely generated T-fuzzy linear spaces is proposed and their structure is roughly studied. Particularly, it is pointed out that if X is a finite dimensional real or complex Euclidean space, every Min-fuzzy linear space in X (i.e., fuzzy subspace of X in the sense of Katsaras and Liu [1]) is finitely generated. In Section 4, a definition is given of simply generated T-fuzzy linear spaces and it is shown that every finitely generated T-fuzzy linear space can be decomposed into a finite number of simply generated T-fuzzy linear spaces. Finally, in Section 5, the concepts are introduced of T-equivalence and congruence for finite families of fuzzy points and a sufficient condition for them to be T-equivalent is given. Besides this, for the case that T is a strict t-norm, it is shown that under an appropriate assumption, the condition is also necessary.