In this paper a simple and effective expert system to predict random data fluctuation in short-term period is established. Evaluation process includes introducing Fourier series, Markov chain model prediction and comparison (Gray) combined with the model prediction Gray- Fourier- Markov that the mixed results, to create an expert system predicted with artificial intelligence, made this model to predict the effectiveness of random fluctuation in most data management programs to increase. The outcome of this study introduced artificial intelligence algorithms that help detect that the computer environment to create a system that experts predict the short-term and unstable situation happens correctly and accurately predict. To test the effectiveness of the algorithm presented studies (Chen Tzay len,2008), and predicted data of tourism demand for Iran model is used. Results for the two countries show output model has high accuracy.