Investigating gender differences based on emotional changes becomes essential to understand various human behaviors in our daily life. Ten students from the University of Vienna have been recruited by recording the electroencephalogram (EEG) dataset while watching four short emotional video clips (anger, happiness, sadness, and neutral) of audiovisual stimuli. In this study, conventional filter and wavelet (WT) denoising techniques were applied as a preprocessing stage and Hurst exponent $\left(\mathrm{Hur}\right)$ and amplitude-aware permutation entropy $\left(\mathrm{AAPE}\right)$ features were extracted from the EEG dataset. $k$ -nearest neighbors $\left(\text{kNN}\right)$ and support vector machine (SVM) classification techniques were considered for automatic gender recognition from emotional-based EEGs. The main novelty of this paper is twofold: first, to investigate $\mathrm{Hur}$ as a complexity feature and $\mathrm{AAPE}$ as an irregularity parameter for the emotional-based EEGs using two-way analysis of variance (ANOVA) and then integrating these features to propose a new $\mathrm{CompEn}$ hybrid feature fusion method towards developing the novel $\text{WT}\_\mathrm{CompEn}$ gender recognition framework as a core for an automated gender recognition model to be sensitive for identifying gender roles in the brain-emotion relationship for females and males. The results illustrated the effectiveness of $\mathrm{Hur}$ and $\mathrm{AAPE}$ features as remarkable indices for investigating gender-based anger, sadness, happiness, and neutral emotional state. Moreover, the proposed $\text{WT}\_\mathrm{CompEn}$ framework achieved significant enhancement in SVM classification accuracy of 100%, indicating that the novel $\text{WT}\_\mathrm{CompEn}$ may offer a useful way for reliable enhancement of gender recognition of different emotional states. Therefore, the novel $\text{WT}\_\mathrm{CompEn}$ framework is a crucial goal for improving the process of automatic gender recognition from emotional-based EEG signals allowing for more comprehensive insights to understand various gender differences and human behavior effects of an intervention on the brain.