Fuzzy Set

Audio signal processing is moving towards detecting and/or defining rare/anomalous sounds. The application of such an anomaly detection problem can be easily extended to audio surveillance systems. Thus, a rare sound event detection method for road traffic monitoring is proposed in this paper, including detection of hazardous events, i.e., road accidents. The method is based on combining anomaly detection techniques, such as variational autoencoders (VAE) and Interval-valued fuzzy sets. The VAE is used to calculate the reconstruction error of the input audio segment. Based on this reconstruction error, a fuzzy membership function, composed of an optimistic/upper component and a pessimistic/lower component, is calculated. Finally, a probabilistic method for interval comparison is used to calculate the membership score, hence to evaluate the interval-valued fuzzy sets. Finally, classification into anomalous/normal events is obtained by defuzzification. Results show that with a careful parameter setting, the proposed method outperforms the state-of-the-art one-class SVM for anomaly detection.

This paper addresses state estimation of discrete event systems (DES) modeled by fuzzy timed Petri nets (FTPN). A definition of FTPN in which fuzzy sets, associated to places, represent the ending time uncertainty of activities is presented; then the fuzzy state equation composed by a set of matrix expressions is developed, allowing computing the marking evolution of DES exhibiting cyclic behavior. A method for approximating the marking of strongly connected state machines is proposed.