Abstract: In real social life, the game strategy or profits with players involved is a variables mapping problem, such as time, space, environment, system or other related variables. From the angle of grey information variable, in this paper, the concept is given and the representation of functional interval grey number is designed. What's more, comparison and arithmetic rules between them are provided. Analysing and describing the form and frame of uncertain information based functional game problems can show the game features, properties and strategic form. Using optimization theory and its related technology to design the optimization algorithm based on uncertain information, not only ways to solve uncertain information problem in real life are provided, but also gives a new method for reference is proposed to solve the practical problems. Finally, by means of computer simulation, a case of " piracy and anti-piracy " provides a detailed comparative analysis which illustrates the scientificity and the accuracy of the information based variable functional game model.

Key words: grey information variable, interval grey numbers, functional game