This paper discusses a class of intuitionistic fuzzy interval linear programming problems with interval coefficients in both the objective functions and constraints. The noninferior solutions to such problems are defined based on order relations between interval valued intuitionistic fuzzy number, and can be found by solving a parametric nonlinear programming problem. Considering the uncertain returns of assets in capital markets as interval valued intuitionistic fuzzy number, we propose a model for portfolio selection based on the absolute deviation measure of risk, which can be transformed to a nonlinear programming model studied in the paper. The method is illustrated by solving a simplified portfolio selection problem.