Fuzzy Cognitive Maps Learning Research Articles

Enhancing hourly electricity forecasting using fuzzy cognitive maps with sample entropy

Accurate electricity consumption forecasting is the crucial to ensure the stable operation of the power system and optimize the smart grid dispatch. However, existing methods may not effectively capture complex potential features and change patterns, and are susceptible to noise, leading to deficiencies such as suboptimal electricity consumption forecasting accuracy, poor stability, and weak generalization capabilities. To fill this gap, a high order fuzzy cognitive map (FCM) forecasting method based on sample entropy and minimax concave penalty (MCP) regularization is proposed. Firstly, two mode decomposition methods are innovatively fused by utilizing sample entropy to extract the complex features of electricity consumption data, then a high order FCM model with powerful system state prediction capability and interpretable knowledge representation is constructed, and finally a FCM learning method based on MCP regularization is proposed. The forecasting method has the merits of low forecasting error, high stability and strong generalization capabilities. Comprehensive experimental results on multiple electricity consumption datasets show that the proposed method achieves optimal performance compared to 10 state-of-the-art baseline methods, demonstrating effectiveness in the task of electricity consumption forecasting, which contributes to more efficient energy management and cost savings, and provides a reliable tool for smart grid planning and management.

Blind Federated Learning without initial model

Federated learning is an emerging machine learning approach that allows the construction of a model between several participants who hold their own private data. This method is secure and privacy-preserving, suitable for training a machine learning model using sensitive data from different sources, such as hospitals. In this paper, the authors propose two innovative methodologies for Particle Swarm Optimisation-based federated learning of Fuzzy Cognitive Maps in a privacy-preserving way. In addition, one relevant contribution this research includes is the lack of an initial model in the federated learning process, making it effectively blind. This proposal is tested with several open datasets, improving both accuracy and precision.

Sparse and regression learning of large-scale fuzzy cognitive maps based on adaptive loss function

Sparse and regression learning of large-scale fuzzy cognitive maps based on adaptive loss function

Explainable fault prediction using learning fuzzy cognitive maps

AbstractIoT sensors capture different aspects of the environment and generate high throughput data streams. Besides capturing these data streams and reporting the monitoring information, there is significant potential for adopting deep learning to identify valuable insights for predictive preventive maintenance. One specific class of applications involves using Long Short‐Term Memory Networks (LSTMs) to predict faults happening in the near future. However, despite their remarkable performance, LSTMs can be very opaque. This paper deals with this issue by applying Learning Fuzzy Cognitive Maps (LFCMs) for developing simplified auxiliary models that can provide greater transparency. An LSTM model for predicting faults of industrial bearings based on readings from vibration sensors is developed to evaluate the idea. An LFCM is then used to imitate the performance of the baseline LSTM model. Through static and dynamic analyses, we demonstrate that LFCM can highlight (i) which members in a sequence of readings contribute to the prediction result and (ii) which values could be controlled to prevent possible faults. Moreover, we compare LFCM with state‐of‐the‐art methods reported in the literature, including decision trees and SHAP values. The experiments show that LFCM offers some advantages over these methods. Moreover, LFCM, by conducting a what‐if analysis, could provide more information about the black‐box model. To the best of our knowledge, this is the first time LFCMs have been used to simplify a deep learning model to offer greater explainability.

A Review of Fuzzy Cognitive Maps Extensions and Learning

Fuzzy Cognitive Maps (FCM) is a soft computing technique whose vertices and edges are fuzzy values with an inference mechanism for solving modelling problems; it has been used in modelling complex systems like industrial and process control. The concept was first introduced in 1986, with an initial learning algorithm in 1996; several works have been published on FCM methodology, learnings and applications. Fuzzy cognitive maps continue to evolve both in theory, learning algorithms and application. Many theories like intuitionistic theory, hesitancy theory, grey system theory, wavelet theory, etc., are integrated with the conventional FCM. These extensions have improved Fuzzy cognitive Maps to handle problems of uncertainty, incomplete information, hesitancy, dynamic systems and probabilistic fuzzy events. They also strengthen fuzzy cognitive Maps’ modelling power for application in almost any domain. However, the compilation of the development in methodology and adaptation of FCM are either old or omitted some of the recent advances or focused on specific applications of FCM in some areas. This paper reports extension, learning and applications of FCM from the initial conventional FCM to recent extensions and some of the important features of those extensions and learning.

Time series forecasting using fuzzy cognitive maps: a survey

Among various soft computing approaches for time series forecasting, fuzzy cognitive maps (FCMs) have shown remarkable results as a tool to model and analyze the dynamics of complex systems. FCMs have similarities to recurrent neural networks and can be classified as a neuro-fuzzy method. In other words, FCMs are a mixture of fuzzy logic, neural network, and expert system aspects, which act as a powerful tool for simulating and studying the dynamic behavior of complex systems. The most interesting features are knowledge interpretability, dynamic characteristics and learning capability. The goal of this survey paper is mainly to present an overview on the most relevant and recent FCM-based time series forecasting models proposed in the literature. In addition, this article considers an introduction on the fundamentals of FCM model and learning methodologies. Also, this survey provides some ideas for future research to enhance the capabilities of FCM in order to cover some challenges in the real-world experiments such as handling non-stationary data and scalability issues. Moreover, equipping FCMs with fast learning algorithms is one of the major concerns in this area.

Towards improved multifactorial particle swarm optimization learning of fuzzy cognitive maps: A case study on air quality prediction

Fuzzy cognitive map (FCM) is a very simple, efficient, and powerful soft computing tool for modeling and analysis of a complex system. Due to its simplicity and transparency, FCM has been widely utilized in engineering, environment, medicine, and other complex systems. However, it remains challenging to handle dynamic, non-stationary, and noisy time series, such as air quality monitoring data, which is with typical temporal periodicity, cross-interference, low-quality, and great noise. Concerning the above challenges, we propose an improved multifactorial particle swarm optimization learning algorithm of FCM, termed as IMFPSO-FCM. Within the framework of IMFPSO-FCM, the learning of an FCM is regarded as a multitask optimization problem. Every task represents learning local connections of a node, and a single population is adopted to process these tasks simultaneously. The task selection mechanism is used to automatically select appropriate target tasks, thereby suppressing negative transfer and enabling useful information to be transferred between tasks. In addition, a multi-dimensional adaptive inertia weight strategy and a local search strategy are employed to further improve the performance of the model. The performance of IMFPSO-FCM is validated on several public datasets and real-world air quality monitoring datasets. The experimental results demonstrate the performance of the development method and emphasize its practicality.

Learning large-scale fuzzy cognitive maps using an evolutionary many-task algorithm

Fuzzy cognitive maps (FCMs) are a powerful tool for simulating and analyzing complex systems. Many efficient methods based on evolutionary algorithms have been proposed to learn small-scale FCMs. However, large number of function evaluations of those methods make them difficult to cope with large-scale FCM learning problems. To overcome this issue, we propose a random inactivation-based batch many-task evolutionary algorithm, termed as IBMTEA-FCM. Inspired by the probability of knowledge sharing in different tasks, the problem of FCM learning is first modeled as a many-task optimization problem, in which each task represents learning local connections of a node in a single FCM. To ensure the effectiveness of knowledge transfer, all tasks are randomly divided into multiple batches to optimize separately. In this method, an evolutionary many-task framework is employed to overcome the proposed many-task FCM learning problem and we randomly deactivate weighted edges to ensure the sparsity of FCM in the evolutionary process. The performance of IBMTEA-FCM is validated on both synthetic datasets and a practical study of gene regulatory network reconstruction. Compared with existing classical methods, the experimental results show that IBMTEA-FCM can learn large-scale FCMs with higher accuracy and less computational cost.

Risks Analyzing and management in Software Project Management Using Fuzzy Cognitive Maps with Reinforcement Learning

Many projects fail each year simply because a risk has been misjudged, ignored or unidentified. An essential motivation for analyzing the risk of a project is to inform managers in order to reduce the risk, and therefore the loss of the project. Risk analysis can help identify the best actions that would reduce the risk and assess by how much. In the last decades, the Fuzzy Cognitive Map emerged as a powerful tool for modeling and supervising dynamic interactions in complex systems. There is two ways to construct them, the first way by experts of domain and the second way by learning method based on the historical of data. In this paper, we develop a new learning fuzzy cognitive maps based on a reinforcement learning algorithm so called Q-learning and we propose here a new formulation of kosko causality principle. This connection between fuzzy cognitive maps and reinforcement learning allows us to choose based on the historical of data learning process the best and the most important connections between concepts. In this work, we illustrate the effectiveness of the proposed approach by modeling and studying the analysis of project risk management as an economic decision support system.

A Learning Fuzzy Cognitive Map (LFCM) Approach to Predict Student Performance

Aim/Purpose: This research aims to present a brand-new approach for student performance prediction using the Learning Fuzzy Cognitive Map (LFCM) approach. Background: Predicting student academic performance has long been an important research topic in many academic disciplines. Different mathematical models have been employed to predict student performance. Although the available sets of common prediction approaches, such as Artificial Neural Networks (ANN) and regression, work well with large datasets, they face challenges dealing with small sample sizes, limiting their practical applications in real practices. Methodology: Six distinct categories of performance antecedents are adopted here as course characteristics, LMS characteristics, student characteristics, student engagement, student support, and institutional factors, along with measurement items within each category. Furthermore, we assessed the student’s overall performance using three items of student satisfaction score, knowledge construction level, and student GPA. We have collected longitudinal data from 30 postgraduates in four subsequent semesters and analyzed data using the Learning Fuzzy Cognitive Map (LFCM) technique. Contribution: This research proposes a brand new approach, Learning Fuzzy Cognitive Map (LFCM), to predict student performance. Using this approach, we identified the most influential determinants of student performance, such as student engagement. Besides, this research depicts a model of interrelations among the student performance determinants. Findings: The results suggest that the model reasonably predicts the incoming sequence when there is a limited sample size. The results also reveal that students’ total online time and the regularity of learning interval in LMS have the largest effect on overall performance. The student engagement category also has the highest direct effect on student’s overall performance. Recommendations for Practitioners: Academic institutions can use the results and approach developed in this paper to identify students’ performance antecedents, predict the performance, and establish action plans to resolve the shortcomings in the long term. Instructors can adjust their learning methods based on the feedback from students in the short run on the operational level. Recommendation for Researchers: Researchers can use the proposed approach in this research to deal with the problems in other domains, such as using LMS for organizational/institutional education. Besides, they can focus on specific dimensions of the proposed model, such as exploring ways to boost student engagement in the learning process. Impact on Society: Our results revealed that students are at the center of the learning process. The degree to which they are dedicated to learning is the most crucial determinant of the learning outcome. Therefore, learners should consider this finding in order the gain value from the learning process. Future Research: As a potential for future works, the proposed approach could be used in other contexts to test its applicability. Future studies could also improve the performance level of the proposed LFMC model by tuning the model’s elements.

Simulation-based optimization for modeling and mitigating tunnel-induced damages

This research develops a simulation-based optimization approach that is capable of modeling and mitigating tunnel-induced damages. Two fuzzy cognitive maps (FCMs) (i.e., one with self-feedback and the other without self-feedback) are learned from historical datasets by using the real-coded genetic algorithm (RCGA) on a data-driven modeling manner. Then, the optimal variable value set is searched in the input space. Two new measures, namely “maximum response” and “average response”, are proposed to search the optimal variable value set in the input space in the FCM dynamic simulation process. A realistic tunnel case in the Wuhan metro system in China is extensively investigated to demonstrate the applicability and effectiveness of the developed approach. Results indicate that (1) The FCM with self-feedback is more stable than the FCM without self-feedback considering its higher coefficient of determination in the testing samples, where less modification of input variables realizes comparable improvement in the objective in the FCM with self-feedback. (2) The measure “maximum response” shows a larger change in the objective than the measure “average response”, where modifications in input space are similar. (3) It is revealed that the ground settlement is more sensitive to TBM operational parameters than tunnel geometry and geological conditions in the two learned FCMs. The developed approach provides insights into a better understanding of causal relationships among factors in tunnel-induced damages, enabling the planning of proactive control strategies for mitigating tunnel-induced damages.

Pseudoinverse learning of Fuzzy Cognitive Maps for multivariate time series forecasting

Forecasting multivariate time series is an important problem considered in many real-world scenarios. To deal with that problem, several forecasting models have already been proposed, where Fuzzy Cognitive Maps (FCMs) are proved to be a suitable alternative. The key limitation of the existing FCM-based forecasting models is the lack of time-efficient learning algorithms. In this paper, we plug that gap by proposing a new FCM learning algorithm which is based on Moore–Penrose inverse. Moreover, we propose an innovative approach that equips FCM with long-term, multistep prediction capabilities. A huge advantage of our method is the lack of parameters which in the case of competitive approaches require laborious adjustment or tuning. The other added value of our method is the reduction of the processing time required to train FCM. The performed experiments revealed that FCM trained using our method outperforms the best FCM-based forecasting model reported in the literature.

CNN-FCM: System modeling promotes stability of deep learning in time series prediction

Time series data are usually non-stationary and evolve over time. Even if deep learning has been found effective in dealing with sequential data, the stability of deep neural networks in coping with the situations unseen during the training stage is also important. This paper deals with this problem based on a fuzzy cognitive block (FCB) which embeds the learning of high-order fuzzy cognitive maps into the deep learning architecture. Thereafter, computers can automatically model the complex system that produces the observation rather than simply regress the available data. Respectively, we design a deep neural network termed CNN-FCM which has combined the available convolution network with FCB. To validate the advantages of our design and verify the effectiveness of FCB, twelve benchmark datasets are employed and classic deep learning architectures are introduced as the comparison. The experimental results show that the performance of many current popular deep learning architectures declines when handling data deviated from the training set. FCB plays an important role in promoting the performance of CNN-FCM in the corresponding experiments. Thereafter, we conclude that system modeling can promote the stability of deep learning in time series prediction.

Online Fuzzy Cognitive Map Learning

The fuzzy cognitive map (FCM) is an effective tool for modeling and simulating complex dynamic systems. The research on the problem of learning FCM from the available time series is outstanding. Many batch FCM learning methods have been proposed to address this issue and the performance of these methods is satisfactory. However, these batch-learning methods are difficult to cope with large-scale data sets (for example, the memory in computers is not enough to store all instances) and real-time streaming data, leading to the failure of real-time and online analysis of complex systems. In this article, unlike the existing batch learning methods, such as evolutionary and regression-based methods, we first extend the FCM learning to an online setting, and then develop an effective algorithm based on a follow-the-regularized-leader (FTRL)-proximal style learning algorithm to address the online FCM learning problem, termed as OFCM. The performance of OFCM is validated on constructed benchmark data sets, including synthetic data sets, and gene regulatory network reconstruction data sets. The experimental results demonstrate the merits of OFCM, which can effectively solve online FCM learning problems.

A Preference-Based Evolutionary Biobjective Approach for Learning Large-Scale Fuzzy Cognitive Maps: An Application to Gene Regulatory Network Reconstruction

Learning large-scale fuzzy cognitive maps (FCMs) with the sparse attribute automatically from time series without prior knowledge remains a challenging problem. Most existing automated learning methods were applied to learn small-scale FCMs, and the learned FCMs are much denser than the maps constructed by human experts. Learning FCMs is the procedure of judging whether there are connecting edges and determining the weights of connecting edges. Thus, we transform the problem of learning FCMs into a biobjective optimization problem with two objects of minimizing the measure error and the number of nonzero entries, respectively. To solve this optimization problem, a preference-based iterative thresholding evolutionary biobjective optimization algorithm for learning FCMs is proposed. The strategy focuses on the knee area of the Pareto front (PF) with preference on the solutions near the true sparsity. Moreover, an initialization operator based on random forest is proposed to increase the speed of convergence toward the PF. The experiments on large-scale synthetic data with varying sizes and densities and the application to the gene regulatory network reconstruction problem have been conducted to demonstrate that our proposal matches or exceeds the existing state-of-the-art FCM learning approaches in most cases in terms of four measures, namely, Data_Error , Out_of_Sample_Error , Model Error, and SS_Mean . The Data_Error obtained by the proposed method can achieve 3.07E-06 even when the number of nodes reaches 200. We also demonstrate the effectiveness of the proposed initialization operator and the preference-based strategy, which can result in a fast convergence speed and higher accuracy.

Deterministic learning of hybrid Fuzzy Cognitive Maps and network reduction approaches

Hybrid artificial intelligence deals with the construction of intelligent systems by relying on both human knowledge and historical data records. In this paper, we approach this problem from a neural perspective, particularly when modeling and simulating dynamic systems. Firstly, we propose a Fuzzy Cognitive Map architecture in which experts are requested to define the interaction among the input neurons. As a second contribution, we introduce a fast and deterministic learning rule to compute the weights among input and output neurons. This parameterless learning method is based on the Moore–Penrose inverse and it can be performed in a single step. In addition, we discuss a model to determine the relevance of weights, which allows us to better understand the system. Last but not least, we introduce two calibration methods to adjust the model after the removal of potentially superfluous weights.

Evolutionary multitasking fuzzy cognitive map learning

In real-world applications, there exist multiple fuzzy cognitive maps (FCMs) learning tasks with similar attributes that have to be optimized simultaneously, however, all existing algorithms were designed to learn single FCM without considering the valuable patterns that can share with each other. For the purpose of making use of similar structure patterns among different tasks, we introduce the evolutionary multitasking framework to learn different FCMs at one time by taking each FCM learning problem as a task. Most proposed evolutionary-based algorithms learn FCMs from time series by minimizing data error which evaluates the difference between generated response sequences and available response sequences, which did not take the sparsity of the weight matrix into consideration. To learn large-scale FCMs for each task, in this paper we adopt a decomposition strategy based multiobjective optimization algorithm considering both the measure error and sparsity of FCMs. Moreover, the memetic algorithm and LASSO initialization operator are incorporated into the multitasking framework to improve the performance and accelerate the convergence. Through the whole process, we find that multitasking optimization can not only learn various FCMs in a population but also improve the accuracy of similar tasks by taking the advantage of gene transfer for similar patterns. Extensive experiments on two-task FCM learning problems with varying number of nodes, densities and activation functions and the application for the problem of reconstructing gene regulatory networks have been conducted to illustrate that the proposal can learn large-scale FCMs with low errors in a fast convergence speed.

An adaptive fusion of infrared and visible image based on learning of sparse fuzzy cognitive maps on compressive sensing

In the recent trends of image processing, simultaneous image compression and fusion has become the major subject of interest. The advantage of image compression is that, it reduces the storage space and also reduces the bandwidth required for transmission. To get a high detailed compressed image, the fusion of visible and infrared images of the same scene is required. Infrared images provide hidden targets of the scene whereas visible images provide texture details of the scene. Hence if these two images are fused then it is possible to obtain a highly detailed image with all the hidden targets of the scene. This paper presents a novel method of visible and infrared image fusion based on compressed sensing and fuzzy logic. The visible and infrared images are converted with the Daubechies wavelet to decompose into lower and higher sub bands. The lower sub band is fused using maximum fusion rule, whereas the higher sub-bands are fused using effective type 2 fuzzy logic-based fusion rule. OOMP is used for retrieval of fused measured values into recovered sub-bands. The recovered higher and lower sub bands are reconstructed employing inverse discrete wavelet transform. The recommended technique is evaluated with several parameters such as Peak Signal Noise Ratio, Mean Square Error, Entropy, Mutual information, Standard deviation, Time and Compression Ratio. The results are compared to the existing techniques which show that the proposed method has a low computational complexity which produces a high detailed fused image with well-preserved edges.

Fast and Effective Learning for Fuzzy Cognitive Maps: A Method Based on Solving Constrained Convex Optimization Problems

The learning of fuzzy cognitive maps (FCMs) is a timely issue pursued by numerous researchers. Many learning methods, such as population-based algorithms and some hybrid algorithms, have been developed and applied to many fields resulting in better performance. However, those learning algorithms also exhibit obvious limitations: some of them either are difficult to handle the learning problem of large-scale FCM or extremely time-consuming with high computational overload. Furthermore, the learning problem of FCM with noisy data is rarely considered in existing algorithms. In this article, a fast and efficient method for learning FCM is proposed. It first transforms the learning problem of the FCM into a convex optimization problem with constraints, and then, the classic interior-point methods are invoked to solve the optimization problem to obtain the optimized weight matrix of the FCM. A series of experiments involving synthetic data, noisy synthetic data, real data, and publicly available data with noise are considered to demonstrate that the proposed method can rapidly and efficiently learn small-scale and large-scale FCMs and deal with the problem of learning FCM from noisy historical data.

Learning fuzzy cognitive maps with convergence using a multi-agent genetic algorithm

Fuzzy cognitive maps (FCMs) are generally applied to model and analyze complex dynamical systems. Recently, many evolutionary-based algorithms are proposed to learn FCMs from historical data by optimizing Data_Error, which is used to evaluate the difference between available response sequences and generated response sequences. However, when Data_Error is adopted as the fitness function for learning FCMs, two problems arise. One is that the optimization reaches the desired result slowly; the other is that the learned FCMs have high link density. To solve these problems, we propose another objective named as convergence error, which is inspired by the convergence of FCMs, to evaluate the difference between the convergent value of available response sequences and that of generated response sequences. In addition, a multi-agent genetic algorithm (MAGA), which is effective for large-scale global numerical optimization, is adopted to optimize convergence error for learning FCMs. To this end, a novel learning approach, a multi-agent genetic algorithm based on the convergence error (MAGA-Convergence), is proposed for learning FCMs. MAGA-Convergence needs less data, because the only initial value and convergent value of the available response sequences are needed for learning FCMs. In the experiments, MAGA-Convergence is applied to learn the FCMs of synthetic data and the benchmarks DREAM3 and DREAM4 for gene regulatory network reconstruction. The experimental results show that the learned FCMs are sparse and could be learned in much fewer generations than other learning algorithms.