The notion of triangular fuzzy number is put forward on the basis of intuitionistic fuzzy sense. The basic algebra and some non-linear operations of triangular intuitionistic fuzzy numbers (TIFNs) are devised. The average ranking index is introduced to find out order relations between two TIFNs. A method is described to approximate a TIFN to a nearly approximated interval number. Applying this result and using interval arithmetic a bound unconstrained optimisation problem is solved whose coefficients are fixed TIFNs. Numerical examples are also given for illustration.