Knowledge graphs are regarded as structured knowledge bases that embody various facts coming from the real world. Their completeness is still far from satisfactory. Relational learning models in link prediction can automatically find the missing relationships between entities to increase the integrality of the knowledge bases, which form two categories purely embedding-based and hybrid embedding-based. Several models including HolE and RotatE belong to purely embedding-based with inefficient performers and few element interactions. Based on the above, this paper advances a novel Knowledge Graph Embedding relational model that leverages a circular correlation operation in the complex domain and dubs as CircularE, which increases interactions between entities and relations to a great extent by this compressed operator without expanding the dimension of space. It gives expression of the interactions between element semantics to achieve good performance in relational learning. Besides, a self-adaption adversarial negative sampling scheme is proposed on account of the KGs structure and the probability semantic of the triples. This negative sampler efficiently optimizes the knowledge representation capability of CircularE and far more than enhances the outputs of several relational original models in embedding-based. Experiments indicate that the competitive properties of CircularE on the four large-scale benchmarks of knowledge base completion tasks are superior to the state-of-the-art methods.

Recently, granular models have been highlighted in system modeling and applied to many fields since their outcomes are information granules supporting human-centric comprehension and reasoning. In this study, a design method of granular model driven by hyper-box iteration granulation is proposed. The method is composed mainly of partition of input space, formation of input hyper-box information granules with confidence levels, and granulation of output data corresponding to input hyper-box information granules. Among them, the formation of input hyper-box information granules is realized through performing the hyper-box iteration granulation algorithm governed by information granularity on input space, and the granulation of out data corresponding to input hyper-box information granules is completed by the improved principle of justifiable granularity to produce triangular fuzzy information granules. Compared with the existing granular models, the resulting one can yield the more accurate numeric and preferable granular outcomes simultaneously. Experiments completed on the synthetic and publicly available datasets demonstrate the superiority of the granular model designed by the proposed method at granular and numeric levels. Also, the impact of parameters involved in the proposed design method on the performance of ensuing granular model is explored.

The change of amplitude and frequency result in a variety of variation modality of time series in the universe. It is difficult to describe the variation features of time series exactly relying solely on a single simulating model. To overcome this limitation, a new prediction model using fuzzy cognitive maps is proposed based on partitioning strategies. Initially, fuzzy c-mean clustering is adopted to partition time series into several sub-sequences. Consequently, each partition has its corresponding sequences. Subsequently these sub-sequences are used to constructed fuzzy cognitive maps models respectively. Finally, the fuzzy cognitive maps models are merged by fuzzy rules. The constructed model is not only performing well in numerical prediction but also has interpretability. The experimental results show that the model based on partition strategy is superior to the single.

Numerous learning methods for fuzzy cognitive maps (FCMs), such as the Hebbian-based and the population-based learning methods, have been developed for modeling and simulating dynamic systems. However, these methods are faced with several obvious limitations. Most of these models are extremely time consuming when learning the large-scale FCMs with hundreds of nodes. Furthermore, the FCMs learned by those algorithms lack robustness when the experimental data contain noise. In addition, reasonable distribution of the weights is rarely considered in these algorithms, which could result in the reduction of the performance of the resulting FCM. In this article, a straightforward, rapid, and robust learning method is proposed to learn FCMs from noisy data, especially, to learn large-scale FCMs. The crux of the proposed algorithm is to equivalently transform the learning problem of FCMs to a classic-constrained convex optimization problem in which the least-squares term ensures the robustness of the well-learned FCM and the maximum entropy term regularizes the distribution of the weights of the well-learned FCM. A series of experiments covering two frequently used activation functions (the sigmoid and hyperbolic tangent functions) are performed on both synthetic datasets with noise and real-world datasets. The experimental results show that the proposed method is rapid and robust against data containing noise and that the well-learned weights have better distribution. In addition, the FCMs learned by the proposed method also exhibit superior performance in comparison with the existing methods.

As an augmentation of classic fuzzy models, granular fuzzy models (GFMs) have been applied to many fields being in rapport with experimental data, models, and users. However, most of the existing methods used to construct GFMs are based on the principle of optimal allocation of information granularity, which requires that a numeric model be provided in advance. In this paper, a straightforward and convincing modeling method is proposed to directly construct GFM on a basis of experimental data. The method first granulates the output space to form some interval information granules with distinct semantics and then uses them to partition the entire input space into a series of input subspaces. Subsequently, an initial GFM is emerged by using "If-Then" rules to relate with those interval information granules positioned in the output space and structures expressed in prototypes that are produced by clustering individual input subspaces. Further, the initial GFM is also refined by continuously migrating prototypes in individual input subspaces. The experimental studies using the synthetic dataset and several real-world datasets are reported. They offer a useful insight into the feasibility and effectiveness of the proposed modeling method and reveal the impact of parameters on the performance of the ensuing GFMs. An application example is also presented to exhibit the advantages of the resulting GFM.

Information granules are fundamental, abstract, and easy-to-operate constructs supporting the human-centered handling way in granular computing (GrC). One of the basic properties of information granules comes with its hierarchy. Information granularity is the quantification expression of hierarchy of an information granule. Forming information granules with multigranularity to hierarchically describe the nature of data is an important task in GrC. In this article, a cone-shaped fuzzy set-based granular description method with multigranularity is proposed for multidimensional data. Its fundamental idea is to realize the synergy of quantification of information granularity and a hierarchical description of data by means of α-cuts of cone-shaped fuzzy sets. The proposed method first partition the entire data set into a series of data chunks. Then, some mutually nonoverlapping cone-shaped fuzzy sets are constructed by optimally determining their cores and support radii in terms of the coverage of α-cuts of these fuzzy sets to the data located in individual chunks and the corresponding specificity. Finally, by implementing α-cuts processing for these constructed cone-shaped fuzzy sets, a collection of families of hyper-spherical information granules used to hierarchically describe the structural characteristics of the data set are completely emerged. Besides, the quality of the resulting families of hyper-spherical information granules is evaluated along the granular perspective and the application perspective, respectively. A series of experimental studies concerning several synthetic and publicly available data sets are covered. The experimental results demonstrate the superiority of the proposed granular description method of data with multigranularity.

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.

Interval-valued time series (ITS) are interval-valued data that are collected in chronological order. The modeling of ITS is an ongoing issue in domain of time series analysis. This paper presents a new modeling method of ITS based on the synergy of fuzzy set theory and artificial neural networks. The proposed method involves the construction of collection of fuzzy sets describing characteristics of amplitude of ITS, the expression and reconstruction mechanism of ITS and the emergence of model of ITS based on artificial neural network (ANN). The resulting model of ITS not only supports the linguistic output but also the numeric output in interval format. A series of experimental studies is reported for two publicly available financial datasets showing different dynamic characteristics. Experimental results clearly show that the constructed ITS model has the better performance on the linguistic and numeric level.

At present, the development of most of the granular fuzzy models depends upon some well-established numeric ones. In this study, a layered approach used to directly construct granular fuzzy models based on multidimensional numeric data is presented by engaging design methodology of granular computing. The crux of the approach involves a construction of interval information granules in the output space and the corresponding hyperbox information granules in the input space. A method of constructing these information granules and the hyperbox-based granular fuzzy model formed around them is studied in detail. Two different schemes to decode the formed hyperbox-based granular fuzzy model are also presented. Furthermore, a measure of a composite quality of the formed hyperbox-based granular fuzzy model is proposed along with the concept of coverage and specificity of resulting information granules. A number of experimental studies are reported, which offer a useful insight into the effectiveness of the presented approach, as well as reveal the impact of critical parameters on the performance of the established models.

In this paper, a fuzzy c-means clustering algorithm based on interval-valued weights is proposed for improving clustering performance. In the proposed algorithm, the interval-valued weights are first constructed by synergy of the ReliefF algorithm and the analytic hierarchy process (AHP) method, and then they are transformed into a constraint condition associating with each weight variable in the weighted clustering objective function. In the sequence, the weighted clustering objective function is solved by combining the Lagrange multiplier method with the gradient-based iteration computation. In the whole process of algorithm iteration, a compulsion strategy with human–computer cooperation is adopted to ensure each weight variable satisfies interval constraint itself. Three well-known data set are used to perform profound experiments. Experimental results clearly show that the proposed algorithm has better clustering performance than other the weighted fuzzy c-means clustering algorithm.

Most researchers of time series forecasting devote to design and develop quantitative models for pursuing high accuracy of forecasting on the numerical level. However, in real world, the numerical accuracy is sometimes not necessary for human cognition and decision-making and the numerical results of forecasting based on quantitative model are deficient in interpretability, thus the development of qualitative forecasting model of time series becomes an evident challenge. In this paper, the improved fuzzy cognitive map (IFCM) are proposed first, and then it is applied to develop qualitative model for linguistic forecasting of time series together with fuzzy c-means clustering technology and real-coded genetic algorithm (RCGA). Two real life time series are used to test the developed forecasting model and compare with another method based on FCM, whose results show the developed FCM forecasting model is more simpler and high quality on the linguistic level.