Epileptic seizures are one of the most crucial neurological disorders, and their early diagnosis will help the clinicians to provide accurate treatment for the patients. The electroencephalogram (EEG) signals are widely used for epileptic seizures detection, which provides specialists with substantial information about the functioning of the brain. In this paper, a novel diagnostic procedure using fuzzy theory and deep learning techniques is introduced. The proposed method is evaluated on the Bonn University dataset with six classification combinations and also on the Freiburg dataset. The tunable-Q wavelet transform (TQWT) is employed to decompose the EEG signals into different sub-bands. In the feature extraction step, 13 different fuzzy entropies are calculated from different sub-bands of TQWT, and their computational complexities are calculated to help researchers choose the best set for various tasks. In the following, an autoencoder (AE) with six layers is employed for dimensionality reduction. Finally, the standard adaptive neuro-fuzzy inference system (ANFIS), and also its variants with grasshopper optimization algorithm (ANFIS-GOA), particle swarm optimization (ANFIS-PSO), and breeding swarm optimization (ANFIS-BS) methods are used for classification. Using our proposed method, ANFIS-BS method has obtained an accuracy of 99.74% in classifying into two classes and an accuracy of 99.46% in ternary classification on the Bonn dataset and 99.28% on the Freiburg dataset, reaching state-of-the-art performances on both of them.