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.
In this paper, we introduce and discuss an important class of endeavors of fuzzy modeling, such as fuzzy descriptive models. In a nutshell, the objective of fuzzy descriptive models is to provide with a sound, comprehensible, and relevant description of experimental data at a general level of relationships revealed there. The elements of such models called descriptors are inherently information granules as the notion of granularity goes hand-in-hand with the interpretability of the resulting constructs (information granules). This paper elaborates on the use of the language of fuzzy sets that are viewed as generic models of information granules. The development of the information granules is carried out in an interactive manner in which a designer can inspect a structure in a data set in a visual fashion. Such visualization is possible through a suitable visualization vehicle provided by self-organizing maps. The role of the designer is to choose from some already visualized regions of the self-organizing map characterized by a high level of data homogeneity. We provide a new algorithm of constructing membership functions of the information granules (fuzzy sets). In addition to some synthetic data, the study includes a comprehensive descriptive modeling of highly dimensional electrocardiogram data.
This paper contributes to the conceptual and algorithmic framework of information granulation. We revisit the role of information granules that are relevant to several main classes of technical pursuits involving temporal and spatial granulation. A detailed algorithm of information granulation, regarded as an optimization problem reconciling two conflicting design criteria, namely, a specificity of information granules and their experimental relevance (coverage of numeric data), is provided in the paper. The resulting information granules are formalized in the language of set theory (interval analysis). The uniform treatment of data points and data intervals (sets) allows for a recursive application of the algorithm. We assess the quality of information granules through application of the fuzzy c-means (FCM) clustering algorithm. Numerical studies deal with two-dimensional (2D) synthetic data and experimental traffic data.
The study is concerned with a description of large numeric data with the aid of building a limited collection of representative information granules with the objective of capturing the structure of the original data. The proposed development scheme consists of two steps. First, a clustering algorithm characterized by high flexibility of coping with the diverse geometry of data structure and efficient computational overhead is invoked. At the second step, a clustering algorithm applied to the clusters already formed during the first phase, yielding a collection of numeric prototypes is involved and the numeric prototypes produced there are then generalized into their granular prototypes. The quality of granular prototypes is quantified while their build-up is supported by the mechanisms of granular computing such as the principle of justifiable granularity. In this paper, the clustering algorithms of DBSCAN and fuzzy C -means were used in successive phases of the processed approach. The experimental studies concerning synthetic data and publicly available data are covered and the performance of the developed approach is assessed along with a comparative analysis.
Most clustering validity indexes (CVIs) for fuzzy clustering are based upon the fuzzy c-means (FCMs) algorithm, and the effect of these CVIs is limited due to the "uniform effect" of FCM. Besides, main existing CVIs have the problems of incompleteness characterization of separateness and weak performance for noisy datasets. To address these challenges, the multi-granularity fusion (MGF) index is proposed. First, MGF synthetically considers the FCM, possibilistic fuzzy c-means and kernel-based FCM algorithms, which is more comprehensive than just considering FCM. Second, we add a perturbation to the sum of the partition matrix as the fuzzy cardinality and combine it with the fuzzy weighted distance, which are helpful to grasp the compactness. Third, four elements are considered together to characterize the separateness, incorporating the minimum distance, the maximum distance, the mean distance, and the sample variance of cluster center, where the last one can make the separateness unbiased from the macroscopic perspective. Besides, the convergence of MGF is proved. Finally, we test MGF for five algorithms on 36 datasets comparing with 14 CVIs, validating the accuracy and stability of MGF. It is observed that MGF can get superior results than other CVIs, especially for high-dimensional datasets and noisy datasets.
Deep fuzzy neural networks have established a fundamental connection between fuzzy systems and deep learning networks, serving as a crucial bridge between two research fields in computational intelligence. These hybrid networks have powerful learning capability stemming from deep neural networks while leveraging the advantages of fuzzy systems, such as robustness. Due to these benefits, deep fuzzy neural networks have recently been an emerging topic in computational intelligence. With the help of deep learning, fuzzy systems have achieved great performance on the classification task. Although fuzzy systems have been extensively investigated, they still struggle in terms of image classification. In this paper, we propose a convolutional fuzzy neural network that combines improved convolutional neural networks with a fuzzy-set-based fusion technique. Different from convolutional neural networks, filters are randomly generated in convolutional layers in our model. This operation not only leads to the fast learning of the model but also avoids some notorious problems of gradient descent procedures in conventional deep learning methods. Extensive experiments demonstrate that the proposed approach is competitive with state-of-the-art fuzzy models and deep learning models. Compared to classical deep models that require massive training data, the proposed approach works well on small datasets.
Due to the characteristic differences of decision makers (DMs), such as growth experience, educational background, social status, and personal beliefs, individual decision information often varies. It becomes more prominent in large-scale group decision making (LSGDM). Therefore, consensus discussion is necessary to make the final decision result represent all DMs' opinions as much as possible. In this regard, this article analyzes the conflicts between individual and subgroup adjustments and between subgroup and group adjustments by the built models. Concerning intrasubgroup adjustment surplus and intersubgroup adjustment surplus, we regard them as cost allocation problems in cooperative games under the consensus constraint. Then, the two-stage Nash-bargaining consensus adjustment game (NBCAG) is introduced to make the allocation result as fair as possible. Meanwhile, the Nash-bargaining consensus adjustment scheme for LSGDM is proposed. Considering the heterogeneity of DMs and subgroups, two-stage asymmetrical NBCAGs are further constructed. In light of these results, a new LSGDM method is proposed. Numerical and comparative analysis is also performed. This article offers the first LSGDM method that emphasizes the fairness and Pareto optimality of consensus adjustment by two-stage Nash-bargaining games.
