Publications

In this study we consider the classification (supervised learning) problem in [0 1]n that utilizes fuzzy sets as pattern classes. Each class is described by one or more fuzzy hyperbox defined by their corresponding minimum- and maximum vertices and t

In this study, we propose a concept of fuzzy wavelet polynomial neural networks (FWPNNs) based on concepts and constructs of polynomial neural networks and fuzzy wavelet neurons (FWNs). These networks exhibit a rule-based architecture while each rule in the FWN consists of the premise part and consequence part. The premise part is realized by using C-means clustering method, while the consequence part is realized by means of wavelet functions whose parameters are estimated with the aid of the least square method. In some sense, the FWPNN can be regarded as a generalized fuzzy wavelet neural network (FWNN). Unlike Gaussian membership functions that are commonly utilized to implement the premise part of the rules in typical FWNNs, C-means method is employed here to overcome a possible curse of dimensionality. Polynomial neural networks (PNNs) are used to express the nonlinearity of a complex system. Furthermore, the particle swarm optimization is used to optimize the design parameters of the proposed network. Based on the PNNs and FWNNs, the proposed FWPNNs take advantages of these two neural networks: it exhibits the abilities to describe high-order nonlinear relations between input and output variables and it is beneficial to describe models impacted by uncertainty. The proposed FWPNNs are applied for time-series prediction and regression problems (e.g., control of dynamic plants). Several well-known modeling benchmarks including regression and time series are considered to evaluate the performance of the proposed FWPNNs. A comparative analysis shows that the proposed FWPNNs result in better performance when comparing with some previous models reported in the literature.

Image denoising technologies in a Euclidean domain have achieved good results and are becoming mature. However, in recent years, many real-world applications encountered in computer vision and geometric modeling involve image data defined in irregular domains modeled by huge graphs, which results in the problem on how to solve image denoising problems defined on graphs. In this paper, we propose a novel model for removing mixed or unknown noise in images on graphs. The objective is to minimize the sum of a weighted fidelity term and a sparse regularization term that additionally utilizes wavelet frame transform on graphs to retain feature details of images defined on graphs. Specifically, the weighted fidelity term with ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm and ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm is designed based on a analysis of the distribution of mixed noise. The augmented Lagrangian and accelerated proximal gradient methods are employed to achieve the optimal solution to the problem. Finally, some supporting numerical results and comparative analyses with other denoising algorithms are provided. It is noted that we investigate image denoising with unknown noise or a wide range of mixed noise, especially the mixture of Poisson, Gaussian, and impulse noise. Experimental results reported for synthetic and real images on graphs demonstrate that the proposed method is effective and efficient, and exhibits better performance for the removal of mixed or unknown noise in images on graphs than other denoising algorithms in the literature. The method can effectively remove mixed or unknown noise and retain feature details of images on graphs. It delivers a new avenue for denoising images in irregular domains.

Purpose Bounds on the rate of convergence of learning processes based on random samples and probability are one of the essential components of statistical learning theory (SLT). The constructive distribution‐independent bounds on generalization are the cornerstone of constructing support vector machines. Random sets and set‐valued probability are important extensions of random variables and probability, respectively. The paper aims to address these issues. Design/methodology/approach In this study, the bounds on the rate of convergence of learning processes based on random sets and set‐valued probability are discussed. First, the Hoeffding inequality is enhanced based on random sets, and then making use of the key theorem the non‐constructive distribution‐dependent bounds of learning machines based on random sets in set‐valued probability space are revisited. Second, some properties of random sets and set‐valued probability are discussed. Findings In the sequel, the concepts of the annealed entropy, the growth function, and VC dimension of a set of random sets are presented. Finally, the paper establishes the VC dimension theory of SLT based on random sets and set‐valued probability, and then develops the constructive distribution‐independent bounds on the rate of uniform convergence of learning processes. It shows that such bounds are important to the analysis of the generalization abilities of learning machines. Originality/value SLT is considered at present as one of the fundamental theories about small statistical learning.

This article elaborates on the scope of knowledge representation in neural networks. In particular, we identify a list of properties of neural networks that are of interest in the context of data mining.

In this article, we elaborate on a design and realization of fuzzy rule-based model in the horizontal federated learning framework. Traditional machine learning in distributed environment often involves sharing sensitive information with other sites or transferring data to a central server on which a global model is trained. These situations increase the communication overhead and pose serious threats to the privacy of sensitive data. Federated learning opens up the possibility for collaboratively training a global model on a basis of distributed on-site data without sacrificing data privacy. While fuzzy rule-based models have been used in system modeling due to their substantial modeling abilities and good interpretability, the implementation of fuzzy rule-based models in a distributed environment without compromising data privacy still requires careful consideration. This article proposes a two-step federated learning approach to train a global model on a basis of private data located across different sites without their centralization. The first step concerns the determination of the structure of the data through federated collaborative clustering. Subsequently, a shared global model is trained jointly by all the participating clients. An advantage of the proposed method is that it achieves high accuracy without violating data privacy. A series of experimental studies are conducted to gain a detailed insight into the realization steps and demonstrate the effectiveness of the proposed method.

In this study, we introduce and discuss a concept of fuzzy plug‐ins and investigate their role in system modeling. Fuzzy plug‐ins are rule‐based constructs augmenting a given global model (arising in the form of some regression relationship, neural network, etc.) in the sense that they compensate for the mapping errors produced by the global model. The proposed design method develops around information granules of error defined in the output space and the induced fuzzy relations expressed in the space of input variables. The construction of the linguistic granules is carried out with the aid of context‐based fuzzy clustering – a generalized version of the well‐known FCM algorithm that is well‐suited to the design of fuzzy sets and relations being used as a blueprint of the plug‐ins. An overall modeling architecture combining the global model with its plug‐ins is discussed in detail and a complete design procedure is provided. Finally, some illustrative numerical examples are shown as well.

The paradigm of fuzzy modelling entails development of relationships (dependencies) between the linguistic entities defined for system's variables. The key feature of the fuzzy models pertains to their significant flexibility so they could easily be modified to comply with the principle of incompatibility. Considering the existing panoply of fuzzy models one can easily conclude that most of them are embraced under an umbrella of a single conceptual structure. From a functional point of view this structure is perceived as a combination of the two conceptual interfaces and a single processing block aimed at developing calculus of the linguistic labels. The interfaces produce all the links that are necessary to combine the physical (numerical) level of the real-world system with that of a conceptual character realized within the fuzzy model and articulated at the level of the linguistic entities. The presentation will address the main methodological aspects concerning these functional components with a particular emphasis placed on the associated design principles. The main issues dominating the design of the interfaces pertain to the implemented level of information granularity, optimality of linguistic labels, and linguistic-to-numerical transformations. The processing level of the fuzzy modelling will be considered through the use of fuzzy neural networks. These distributed computing structures are highly heterogeneous as they are constructed with the aid of several distinct types of logic-oriented neurons. The advantages of the fuzzy neural networks such as an implicit scheme of knowledge encapsulation that is carried out there will be discussed in detail.