A programming problem with T-fuzzy variations has been widely used in the realistic world because it contains more information than a classical programming. Under cone index J, the author in the paper turns T-fuzzy variations into non-T-fuzzification, so that he turns a linear programming with T-fuzzy variations into a parametric linear programming problem, depending on cone index J, before he can obtain many corresponding properties about a linear programming problem with T-fuzzy variations such as existence of an optimal solution, its determining condition, and duality property. With a numerical example, he verifies the effectiveness of this model and its algorithm.
