This study employs relational analysis and the GreyART network to identify and study the characteristics of electroencephalogram signals of sleep apnea syndrome (SAS). Seventeen raw electroencephalogram data records from the sleep database compiled by Massachusetts Institute of Technology (MIT) and Beth Israel Hospital (BIH) were used in conjunction with four wavelet decomposition steps to obtain the cD4 wavelet coefficient as input for the GreyART network. The GreyART network was then used for simulation training and testing in order to achieve the best recognition results. This study achieved an average recognition rate of 93.33% for electroencephalogram data record slp01b, and recognition rates during the training and testing stage for this record were 95.80% and 92.12%, respectively. This was the best recognition result for any of the 17 records. The overall average recognition rate for all 17 records was 78.10%. In comparison with past literature, this study's use of the GreyART network to recognize electroencephalogram signal characteristics of SAS possesses excellent reference value. To further reduce the costs and the physiological signal measurement items to make it easier for patients to use, this research also proposes to use a single type of physiological signals, electroencephalographic (EEG) signals, as the sole input as identification information to identify SAS diseases. EEG signal detection is utilized because it is nonintrusive, suitable for long-term monitoring and most importantly, it can be used to detect various types of abnormal physiological conditions in SAS, moods, sleep stages, heart rate abnormalities and mental states. In addition, constant monitoring of users in their familiar home environment can also be utilized as self-screening at home to reduce the burden of sleep medicine centers.