The Fuzzy Cognitive Map (FCM) is a powerful model for system state prediction and interpretable knowledge representation. Recent years have witnessed the tremendous efforts devoted to enhancing the basic FCM, such as introducing temporal factors, uncertainty or fuzzy rules to improve interpretation, and introducing fuzzy neural networks or Wavelets to improve time series prediction. But how to achieve high-precision yet interpretable prediction in cross-domain real-life applications remains a great challenge. In this paper, we propose a novel FCM extension called Deep FCM for multivariate time series forecasting, in order to take both the advantage of FCM in interpretation and the advantage of deep neural networks in prediction. Specifically, to improve the predictive power, Deep FCM leverages a fully connected neural network to model connections (relationships) among concepts in a system, and a recurrent neural network to model unknown exogenous factors that have influences on system dynamics. Moreover, to foster model interpretability encumbered by the embedded deep structures, a partial derivative-based approach is proposed to measure the connection strengths between concepts in Deep FCM. An Alternate Function Gradient Descent algorithm is then proposed for parameter inference. The effectiveness of Deep FCM is validated over four publicly available datasets with the presence of seven baselines. Deep FCM indeed provides an important clue to building interpretable predictors for real-life applications.

Intelligent condition monitoring and fault diagnosis by analyzing the sensor data can assure the safety of machinery. Conventional fault diagnosis and classification methods usually implement pretreatments to decrease noise and extract some time domain or frequency domain features from raw time series sensor data. Then, some classifiers are utilized to make diagnosis. However, these conventional fault diagnosis approaches suffer from the expertise of feature selection and they do not consider the temporal coherence of time series data. This paper proposes a fault diagnosis model based on Deep Neural Networks (DNN). The model can directly recognize raw time series sensor data without feature selection and signal processing. It also takes advantage of the temporal coherence of the data. Firstly, raw time series training data collected by sensors are used to train the DNN until the cost function of DNN gets the minimal value; Secondly, test data are used to test the classification accuracy of the DNN on local time series data. Finally, fault diagnosis considering temporal coherence with former time series data is implemented. Experimental results show that the classification accuracy of bearing faults can get 100%. The proposed fault diagnosis approach is effective in recognizing the type of bearing faults.

In order to improve the accuracy of the fault diagnosis of roller bearings, this paper proposes a kind of fault diagnosis algorithm based on manifold learning combined with a wavelet neural network. First, a high-dimensional feature signal set is obtained using a conventional feature extraction algorithm; second, an improved Laplacian characteristic mapping algorithm is proposed to reduce the dimensions of the characteristics and obtain an effective characteristic signal. Finally, the processed characteristic signal is inputted into the constructed wavelet neural network whose output is the types of fault. In the actual experiment of recognizing data sets on roller bearing failures, the validity and accuracy of the method for diagnosing faults was verified.

Fuzzy Cognitive Map (FCM) offers many advantages such intuitive knowledge representation and fast numerical reasoning ability, etc. It suits modeling and decision-making of dynamic systems. With the aims to effectively help to analyze and control system sustainable evolution, the paper defines the steady states of fixed point and limited cycle of a FCM modeling system. Accordingly, the rules of steady states of the FCM model and the factors influencing the steady states are presented and proved. The Three-Rivers represents a system including population, ecological environment, social development and their relationships. Based on the relationships, the Three-Rivers ecosystem is modeled by FCM and the Three-Rivers ecosystemsustainable evolutionis analyzed bythe rules of the steady states of FCM.

Haze-fog has seriously hindered the sustainable development of the ecological environment and caused great harm to the physical and mental health of residents in China. Therefore, it is important to probe the formation of haze-fog for its early warning and prevention. The formation of haze-fog is, in fact, a fuzzy nonlinear process. The formation of haze-fog is such a complex process that it is difficult to simulate its dynamic evolution using traditional methods, mainly because of the lack of their consideration of the nonlinear relationships. It is, therefore, essential to explore new perspectives on the formation of haze-fog. In this work, previous research on haze-fog formation is summarized first. Second, a new perspective is proposed on the application of fuzzy cognitive map to the formation of haze-fog. Third, a data mining method based on the genetic algorithm is used to discover the causality values of a fuzzy cognitive map (FCM) for hazefog formation. Finally, simulation results are obtained through an experiment using the fuzzy cognitive map and its data mining method for the formation of haze-fog. The validity of this approach is determined by definition of a simple rule and the Kappa values. Thus, this research not only provides a new idea using FCM modeling the formation of haze-fog, but also uses an effective method of FCM for solving the nonlinear dynamics of the haze-fog formation.

In order to model multi-dimensions and multi-granularities oriented complex systems, this paper firstly proposes a kind of multi-relational Fuzzy Cognitive Map (FCM) to simulate the multi-relational system and its auto construct algorithm integrating Nonlinear Hebbian Learning (NHL) and Real Code Genetic Algorithm (RCGA). The multi-relational FCM fits to model the complex system with multi-dimensions and multi-granularities. The auto construct algorithm can learn the multi-relational FCM from multi-relational data resources to eliminate human intervention. The Multi-Relational Data Mining (MRDM) algorithm integrates multi-instance oriented NHL and RCGA of FCM. NHL is extended to mine the causal relationships between coarse-granularity concept and its fined-granularity concepts driven by multi-instances in the multi-relational system. RCGA is used to establish high-quality high-level FCM driven by data. The multi-relational FCM and the integrating algorithm have been applied in complex system of Mutagenesis. The experiment demonstrates not only that they get better classification accuracy, but it also shows the causal relationships among the concepts of the system.