Analytic Hierarchy Process (AHP) in Portfolio Selection Based on Information Granularity

Analytic Hierarchy Process (AHP) is a multi criteria decision-making method, which can describe and transform the qualitative problems quantitatively, and then get the quantitative analysis results in accordance with the causal relationship between decision attribute. In this paper, a granular Analytic Hierarchy Process, which introduces the granularity mechanism, is proposed to solve the portfolio selection problem under the mean-risk framework. In the proposed method, the scale value of scheme layer is no longer limited to nine positive integers from 1 to 9, which gives granularity attributes to the comparison of advantages and disadvantages in a specific criterion layer between different schemes. The proposed method reflects small differences between different alternative schemes through granularity attribute, so it can provide rich decision information for decision makers. Three numeric examples from the real-world financial market (China Shanghai Stock Exchange) are provided to illustrate an essence of the proposed method.