In this paper, a fuzzy neural network (FNN) is transformed into an equivalent three-layer fully connected neural inference system (F-CONFIS). This F-CONFIS is a new type of a neural network whose links are with dependent and repeated weights between the input layer and hidden layer. For these special dependent repeated links of the F-CONFIS, some special properties are revealed. A new learning algorithm with these special properties is proposed in this paper for the F-CONFIS. The F-CONFIS is therefore applied for finding the capacity of the FNN. The lower bound and upper bound of the capacity of the FNN can be found from a new theorem proposed in this paper. Several examples are illustrated with satisfactory simulation results for the capacity of the F-CONFIS (or the FNN). These include "within capacity training of the FNN," "over capacity training of the FNN, " "training by increasing the capacity of the FNN," and "impact of the capacity of the FNN in clustering Iris Data." It is noted that the finding of the capacity of the F-CONFIS, or FNN, has its emerging values in all engineering applications using fuzzy neural networks. This is to say that all engineering applications using FNN should not exceed the capacity of the FNN to avoid unexpected results. The clustering of Iris data using FNN illustrated in this paper is one of the most relevant engineering applications in this regards.