Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Fuzzy sets have become popular in every branch of mathematics such as analysis, topology, algebra, applied mathematics etc. Thus fuzzy sets triggered the creation of a wide range of research topics in all areas of science in a short time. In this paper, we use the triangular fuzzy numbers for matrix domains of sequence spaces with infinite matrices. We construct the new space with triangular fuzzy numbers and investigate to structural, topological and algebraic properties of these spaces.