Today, almost all bank affairs are automatic and all transactions, processing and money transfers are performed by applying information systems technologies. Moreover, to codify the strategies and making management decisions more effectively, banks rely on electronic information systems. The remarkable point is the security and the security risk management of information systems which the traditional point of view would not overcome its future challenge. This paper identified the relevant elements to the security risks of informational electronic banking systems based on previous research studies. The final weight of all elements was then determined by fuzzy analytic hierarchy process and Chung weighing method. After that, the final weights of all elements in three case studies from banking section have been calculated. Ultimately, elements securities of those banks were clarified by using Jaeger fuzzy classification. The results indicated that the vulnerability element has the most weight.