In this paper a novel method of ordering intuitionistic fuzzy numbers, based on the notions of ‘value’ and θ-multiple of ‘ambiguity’ of an intuitionistic fuzzy number, is developed. Further, the flexibility parameters, of decision-making at (α, β)-levels, are used in the method. These parameters allow the decision-maker to take decisions at various (α, β)-levels of decision-making. Many a times, all the reasonable properties of ranking intuitionistic fuzzy numbers were never checked in the existing studies. However, in this study an utmost attempt is being made to study the reasonable properties thoroughly. Further, the existing methods are mostly based on intuition and the geometry of the intuitionistic fuzzy numbers. However, the proposed method completely complies with the reasonable properties of ranking intuitionistic fuzzy numbers as well as the coherent intuition and the geometry of the intuitionistic fuzzy numbers. Further, newer properties are also being developed in this study. These prove the novelty of the proposed method. Further, a few numerical examples are discussed that demonstrates the proposed method.