An improved grey relational TOPSIS based on cloud model theory

Abstract

This paper develops an improved TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) based on grey relational analysis and cloud model theory for dealing with the fuzziness and randomness in muti-attribute decision making. Firstly, some concepts of cloud model theory and grey relational analysis were introduced and an improved forward cloud generator was put forward to normalize the decision matrix of TOPSIS, thus the uncertainty of the decision data was embodied and simulated. Then the steps of the improved TOPSIS were described. The calculation method of the numerical characteristics of the cloud model used to normalize the decision matrix was given. The separation to the positive ideal solution and negative ideal solution was calculated by grey relational analysis method which can reflect the trend relationship between the alternative and the ideal solution. The weight of the criteria was calculated on the basis of the exponential scale of analytic hierarchy process. Finally, a numerical example was given to illustrate the practicality and effectiveness of the proposed method. The method can provide more evaluation information by its statistical nature.