In this paper, notion of p-norm generalized trapezoidal intuitionistic fuzzy numbers is introduced. A new ranking method is introduced for p-norm generalized trapezoidal intuitionistic fuzzy numbers. Also, we consider linear programming problem in intuitionistic fuzzy environment. In this problem, all the coefficients and variables are represented by p-norm generalized trapezoidal intuitionistic fuzzy numbers. To overcome the limitations of the existing methods, a  new method is proposed to compute the intuitionistic fuzzy optimal solution for intuitionistic fuzzy linear programming problem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed approach.

intuitionistic fuzzy numbers, linear programming, lexicographic ordering.