This paper proposes a hybrid expert system (HES) to minimise some complexity problems pervasive to the artificial intelligence such as: the knowledge elicitation process, known as the bottleneck of expert systems; the model choice for knowledge representation to code human reasoning; the number of neurons in the hidden layer and the topology used in the connectionist approach; the difficulty to obtain the explanation on how the network arrived to a conclusion. Two algorithms applied to developing of HES are also suggested. One of them is used to train the fuzzy neural network and the other to obtain explanations on how the fuzzy neural network attained a conclusion. To overcome these difficulties the cognitive computing was integrated to the developed system. A case study is presented (e.g. epileptic crisis) with the problem definition and simulations. Results are also discussed.