Abstract
In this paper, we discussed the elementary structure of linear space for triangular fuzzy system, linear subspace of the triangular fuzzy numbers and linear transformations between two triangular fuzzy spaces. We introduce a study of new concept of a Hamel base for any linear space and the uniqueness of its cardinality of fuzzy numbers. We begin with some basic definitions and properties of linear space triangular fuzzy system which will be used throughout this paper. Also the axioms of the primary field and the addition and scalar multiplication operations for triangular fuzzy system have been included.
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