Parallel Learning of Large Fuzzy Cognitive Maps

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.

Fuzzy Cognitive Maps (FCMs) are a causal modelling technique. FCM models contain nodes (representing the concepts to be modelled) and directed weighted edges (representing the causal relations between the concepts). Data-driven FCM learning algorithms are an objective approach with the potential to discover the causal relations that are unknown to human experts. Learning FCM from data can be a difficult problem because the size of the solution space grows quadratically with the number of nodes in the FCM models. A data-driven learning algorithm based on Ant Colony Optimization (ACO) is proposed to develop Fuzzy Cognitive Maps (FCMs). The FCM models can be isomorphically represented as weight vectors. The objective function is to minimize the difference between the estimated response of the FCM model and the target response observed from the to-be-modelled system. An ACO algorithm with heuristic information is proposed to find the best FCM model. The performance of the ACO algorithm was tested on both randomly generated data and DREAM4 project data (publicly available in-silico gene expression data). The experiment results show that the ACO algorithm is able to learn FCMs with at least 40 nodes.

Fuzzy cognitive maps (FCMs) are cognition fuzzy influence graphs, which are based on fuzzy logic and neural networks. Many automated learning algorithms have been proposed to reconstruct FCMs from data, but most learned maps using such methods are much denser than those constructed by human experts. To this end, we first model the FCM learning problem as a multiobjective optimization problem, and then propose a multiobjective evolutionary algorithm, labeled as MOEA-FCM, to learn FCM models. MOEA-FCM is able to learn FCMs with varying densities at the same time from input historical data, which can provide candidate solutions with different properties for decision makers. In the experiments, the performance of MOEA-FCM is validated on both synthetic and real data with varying sizes and densities. The experimental results demonstrate the efficiency of MOEA-FCM and show that MOEA-FCM can not only reconstruct FCMs with high accuracy without expert knowledge, but also create a diverse Pareto optimal front which consists of FCMs with varying densities. The significance of this study is that decision makers can choose different FCM models provided by MOEA-FCM based on their practical requirements.

Fuzzy cognitive maps (FCMs) are generally applied to model and analyze complex dynamical systems. However, the accuracy of population-based FCM learning algorithms is relatively low. Boosting is an effective method to improve the accuracy of any learning algorithm. To this end, we combine FCMs with boosting, termed as boosting fuzzy cognitive maps (BFCMs). The BFCM is an extension of FCMs and has a better performance on fast numerical reasoning than FCMs. In this paper, a real-coded genetic algorithm, which is a popular population-based learning algorithm, is improved on mutation operator and applied to learn the BFCM models, termed as RCGA-BFCM. In the experiments, RCGA-BFCM is applied to learn the BFCM from synthetic data with varying sizes and densities. The experimental results show that RCGA-BFCM can learn BFCMs with high accuracy from synthetic data. In addition, the performance of RCGA-BFCM is validated on the benchmark datasets DREAM3 and DREAM4. The experimental results show that RCGA-BFCM outperforms other learning algorithms obviously, which illustrates that RCGA-BFCM can reconstruct gene regulatory networks (GRNs) effectively.

The Fuzzy Cognitive Map (FCM) method was developed by B. Kosko to extend cognitive maps, which are widely used to represent knowledge in the social sciences. Several algorithms have been proposed for training FCMs. The main objective of the training procedure is to nd a setting of FCM weights that will bring the FCM to a desired stable state. This is achieved by minimizing a well-de ned objective function. The established algorithms heavily depend on the initial approximation of the weight matrix, which is provided by experts. One of the methods for training FCMs is based on particle swarm optimization (PSO). PSO is used to determine the appropriate weight matrices for the system by minimizing a given objective function.

The purposes of this research are to find a model to forecast the electricity consumption in a household based on fuzzy cognitive map (FCM) prediction capabilities. The data analysis has been performed with three different learning algorithms based on the fuzzy cognitive map model which are (a) the multi-step gradient method (MGM), (b) the real coded genetic algorithm (RCGA) and (c) the structure optimization genetic algorithm (SOGA) as a new improvement of the RCGA able to handle the model's complexity investigated in our study. The suitable forecasting methods and two different forecasting periods were chosen by considering the smallest value of MSE (Mean Square Error) and RMSE (Root Mean Square Error), respectively. The proposed FCM-based prediction algorithms were compared with known statistical methods such as ARIMA and artificial intelligent methods such as ANNs and neuro-fuzzy models. The experiments conducted in this study showed that the multi gradient-based algorithm for FCM learning was the most efficient with respect to the accuracy of prediction expressed by the well-known used errors in the two selected forecasting periods.

This paper examines the use of fuzzy cognitive maps (FCMs) as a technique for modeling political and strategic issues situations and supporting the decision-making process in view of an imminent crisis. Its object domain is soft computing using as its basic elements different methods from the areas of fuzzy logic, cognitive maps, neural networks and genetic algorithms. FCMs, more specifically, use notions borrowed from artificial intelligence and combine characteristics of both fuzzy logic and neural networks, in the form of dynamic models that describe a given political setting. The present work proposes the use of the genetically evolved certainty neuron fuzzy cognitive map (GECNFCM) as an extension of certainty neuron fuzzy cognitive maps (CNFCMs) aiming at overcoming the main weaknesses of the latter, namely the recalculation of the weights corresponding to each concept every time a new strategy is adopted. This novel technique combines CNFCMs with genetic algorithms (GAs), the advantage of which lies with their ability to offer the optimal solution without a problem-solving strategy, once the requirements are defined. Using a multiple scenario analysis we demonstrate the value of such a hybrid technique in the context of a model that reflects the political and strategic complexity of the Cyprus issue, as well as the uncertainties involved in it. The issue has been treated on a purely technical level, with distances carefully kept concerning all sides involved in it.

Fuzzy cognitive maps (FCM) are fuzzy signed directed graphs with feedbacks; they are simple and powerful tool for simulation and analysis of complex, nonlinear dynamic systems. However, FCM models are created by human experts mostly, and so built FCM models are subjective and building a FCM model becomes harder as number of variables increases. So in the last decade several methods are proposed providing automated generation of fuzzy cognitive maps from data. The main drawback of the proposed automated methods is their weaknesses on handling with large number of variables. The proposed method brings out a new strategy called concept by concepts approach (CbC) approach for learning of FCM. It enables the generation of large sized FCM models with a high precision and in a rapid way using the historical data.

Fuzzy cognitive maps (FCMs) represent the decision process in the form of a graph that is usually easy to interpret and, therefore, can be applied as a convenient decision-support tool. In the first part of this chapter, we explain the motivations for the research on FCMs and provide a review of the research in this area. Then, as stated in the title of the chapter, we concentrate our attention on the comparative study of adaptive and evolutionary FCMs. The terms adaptive and evolutionary refer to the type of learning applied to obtain a particular FCM. Despite many existing works on FCMs, most of them concentrate on one type of learning method. The purpose of our research is to learn FCMs using diverse methods on the basis of the same dataset and apply them to the same prediction problem. We assume the effectiveness of prediction to be one of the quality measures used to evaluate the trained FCMs. The contribution of this chapter is the theoretical and experimental comparison of adaptive and evolutionary FCMs. The final goal of our research is to determine which of the analyzed learning methods should be recommended for use with respect to the considered prediction problem. To illustrate the predictive capabilities of FCMs, we present an example of their application to the prediction of weather conditions.

Evolutionary learning of fuzzy grey cognitive maps for the forecasting of multivariate, interval-valued time series

Celiac disease (CD) is a complex disorder whose development is affected by genetics (HLA alleles) and gluten ingestion. Its diagnosis is very difficult due to clinical manifestations complexity, latent period, and similarity to other diseases. Studies show that a high percentage of CD patients remain undiagnosed. The celiac patients who are not treated are at a high risk of cancer, malignant lymphoma, and small-bowel neoplasia. Therefore, CD diagnosis and grading is of paramount importance. This paper presents a new method for grading CD based on the combination of fuzzy cognitive map (FCM) and support vector machine. To improve the efficiency and increase classification ability of FCM, particle swarm optimization (PSO) algorithm is applied to adjust FCM weights. In this study, the newest method of grading A, B1, and B2 is used. The empirical results show that the main advantage of PSO algorithm is its speed of convergence and the ability to obtain faster possible schedules. The proposed method is tested on 89 patients. The simulation results prove the superiority of the proposed method compared with Bayesian networks based on the rules and other procedures set forth in the literature. These results show the percentages of 87%, 86%, and 84% for three grades of A, B1 and B2.

The study on the prediction of mine pressure, while exploiting in coal mine, is a critical and technical guarantee for coal mine safety and production. In this paper, primarily due to the actual demand for the prediction of mine pressure, a practical prediction model Mine Pressure Prediction (MPP) was proposed based on fuzzy cognitive maps (FCMs). The Real Coded Genetic Algorithm (RCGA) was proposed to solve the problem by introducing the weight regularization and dropout regularization. A numerical example involving in-situ monitoring data is studied. Mean Square Error (MSE) and fitness function were used to evaluate the applicability of MPP model which is trained by RCGA, Regularization Genetic Algorithm (RGA) and Weight and Dropout RGA optimization algorithms. The numerical results demonstrate that the proposed Weight and Dropout RGA is better than the other two algorithms, and realizing the requirement for prediction of mine pressure in the coal mine production.

Accurate stock prediction is a pressing challenge in quantitative finance, where complex temporal and cross-sectional dynamics defy traditional models. Although deep learning-based methods have made significant progress, most of them focus on individual stock trajectories, neglecting directional causality in stock interactions. Fuzzy cognitive maps (FCMs) are good at modeling the directional causality. Therefore, we design a new type of FCM with each concept node having a fuzzy state vector instead of just a fuzzy state value to more stereoscopic manifest the factors affecting a stock, like firm size, book-to-market value, and market risk emphasized by the famous Fama-French multifactor model. A genetic algorithm with a specially designed objective function is used to learn the new FCMs. Furthermore, the new FCMs are combined with a double-level attention mechanism and graph neural networks (GNNs) for z-score forecasting, named CausalSeqGNN. To balance scalability and adaptability, a dual-phase alternating learning architecture is designed in CausalSeqGNN, where the double-level attention mechanism fuses eight-day price sequences with news-derived sentiment scores updated daily, and the causal matrix capturing asymmetric stock interdependencies obtained by FCM learning updated quarterly since companies generally release their financial reports on a quarterly basis. Successfully synergizing Fama-French-driven causality with temporal dynamics, CausalSeqGNN achieves superior mean squared error and investment performance on US and Chinese market dataset, outperforming state-of-the-art baselines. This hybrid framework offers transformative potential for real-time trading, redefining stock forecasting with unparalleled precision and scalability.

Fuzzy Cognitive Map (FCM) is a soft computing technique for modeling systems. It combines synergistically the theories of neural networks and fuzzy logic. The methodology of developing FCMs is easily adaptable but relies on human experience and knowledge, and thus FCMs exhibit weaknesses and dependence on human experts. The critical dependence on the expert’s opinion and knowledge, and the potential convergence to undesired steady states are deficiencies of FCMs. In order to overcome these deficiencies and improve the efficiency and robustness of FCM a possible solution is the utilization of learning methods. This research work proposes the utilization of the unsupervised Hebbian algorithm to nonlinear units for training FCMs. Using the proposed learning procedure, the FCM modifies its fuzzy causal web as causal patterns change and as experts update their causal knowledge.

A fuzzy cognitive map (FCM) is a graph-based knowledge representation model wherein the connections of the nodes (edges) represent casual relationships between the knowledge items associated with the nodes. This model has been applied to solve various modeling tasks including forecasting time series. In the original FCM-based forecasting model, causal relationships among concepts of the FCM remain unchanged. However, causal relationships may change in time. Therefore, we propose a new learning method for training an FCM resulting in an adaptive FCM which consists of several sub-FCMs. It can select different sub-FCMs at different moments. In an active processing scenario, in which we deal with a large-scale time series with new data being continuously generated, a forecasting model built on the old data should be updated when the new data arrive. Furthermore, retraining an FCM from scratch entails increasing computing overhead that will become a serious obstacle in many practical scenarios. To overcome the above-mentioned shortcomings, this study offers an original design setting in which the FCM is updated by knowledge-guidance learning mechanism for the first time. Compared with the existing classical forecasting models, the proposed model shows higher accuracy and efficiency. Its increased performance is demonstrated through a series of reported experimental studies.