Publications

There have been numerous studies on using the FCM algorithm in clustering and collaboration clustering, especially in data analysis, data mining and pattern recognition. In this study, we present new methods involving interval Type-2 fuzzy sets to realize collaborative clustering. Data in which the clustering results realized at one data site impact clustering carried out at other data sites. Those methods endowed with interval type-2 fuzzy sets help cope with uncertainties present in data. The experiment with weather data sets has shown better results in comparison with the previous approaches.

Purpose The purpose of this paper is to show that exploiting fundamental ideas of granular computing can lead to further conceptual developments of granular metastructures, which are inherently associated with computing involving a large number of individual datasets; and to show that such processing leads to the representatives of information granules and granular models in the form of metastructures and metamodels. Design/methodology/approach The formulation of the concept of granular metastructures is provided and presented along with some essential algorithmic developments and associated optimization strategies. The overall methodological framework is the one of granular computing, especially fuzzy sets and fuzzy sets of higher type. Given the structural facet of optimization, the paper stresses the relevance of the use of evolutionary optimization. Findings This paper focused on the underlying concepts and while it elaborated on some development aspects and optimization tools, it should be stressed that further refinement and a thorough exploitation of optimization techniques in application to the inherently combinatorial facet of the problem are to be pursued in detail. Practical implications The introduced approach and algorithms could be of interest when solving problems of granular metastructures, in particular those encountered in knowledge‐based systems. Originality/value The main aspects of originality concern a formulation of the concept of granular metastructures and their design, based on granular evidence (experimental data) of lower type. A constructive way of forming type‐2 fuzzy sets via the principle of justifiable granularity exhibits a significant level of originality and offers a general way of designing information granules.

In this paper we introduce the use of contextual transformation functions to adjust membership functions in fuzzy systems. We address both linear and nonlinear functions to perform linear or nonlinear context adaptation, respectively. The key issue is to encode knowledge in a standard frame of reference, and have its meaning tuned to the situation by means of an adequate transformation reflecting the influence of context in the interpretation of a concept. Linear context adaptation is simple and fast. Nonlinear context adaptation is more computationally expensive, but due to its nonlinear characteristic, different parts of base membership functions can be stretched or expanded to best fit the desired format. Here we use a genetic algorithm to find a nonlinear transformation function, given the base membership functions and a set of data extracted from the environment classified by means of fuzzy concepts. © 1998 John Wiley & Sons, Inc.

Fuzzy Cognitive Maps are recognized knowledge modeling tool. FCMs are visualized with directed graphs. Nodes represent information, edges represent relations within information. The core element of each Fuzzy Cognitive Map is weights matrix, which contains evaluations of connections between map's nodes. Typically, weights matrix is constructed by experts. Fuzzy Cognitive Map can be also reconstructed in an unmanned mode. In this article authors present their own, new approach to time series modeling with Fuzzy Cognitive Maps. Developed methodology joins Fuzzy Cognitive Map reconstruction procedure with moving window approach to time series prediction. Authors train Fuzzy Cognitive Maps to model and forecast time series. The size of the map corresponds to the moving window size and it informs about the length of historical data, which produces time series model. Developed procedure is illustrated with a series of experiments on three real-life time series. Obtained results are compared with other approaches to time series modeling. The most important contribution of this paper is description of the methodology for time series modeling with Fuzzy Cognitive Maps and moving windows.

In this study, we discuss a concept of shadowed sets and present their applications. To establish some sound compromise between the qualitative Boolean (two-valued) description of data and quantitative membership grades, we introduce an interpretation framework of shadowed sets. Shadowed sets are discussed as three-valued constructs induced by fuzzy sets assuming three values (that could be interpreted as full membership, full exclusion, and uncertain membership). The algorithm of converting membership functions into this quantification is a result of a certain optimization problem guided by the principle of uncertainty localization. We revisit fundamental ideas of relational calculus in the setting of shadowed sets. We demonstrate how shadowed sets help in problems in data interpretation in fuzzy clustering by leading to the three-valued quantification of data structure that consists of core, shadowed, and uncertain structure. © 2008 Wiley Periodicals, Inc.

Abstract The tolerance rough set is developed as one of the outstanding extensions of the Pawlak's rough set model under incomplete information, and the limited tolerance relation is developed to overcome the problem that objects leniently satisfy the tolerance relation. However, the classification based on the limited tolerance relationship cannot reflect the matching degree of uncertain information of objects. In this article, we explore the influence of null values in an incomplete system, and propose the constrained tolerance relation based on the matching degree of uncertain information of objects. The proposed rough set based on the constrained tolerance relation can provide a more detailed structure of an object class through threshold. Proofs and example analyses further show the rationality and superiority of the proposed model.

Neural networks (NNs) with least square error (LSE) estimation form a certain type of single hidden layer feed-forward NNs. In this class of networks, the input connections (weights) and the biases of hidden neurons are generated randomly and fixed after being generated. The output connections are estimated by the LSE method rather than the back-propagation method. The random generation of the input connection weights and the hidden biases results in the larger number of hidden neurons to assure the quality of classification performance. To reduce the number of neurons in the hidden layer while maintaining the classification performance, we apply a "divide and conquer" strategy in this article. In other words, we divide an overall input space into several subspaces by using information granulation technique (Fuzzy C-Means clustering algorithm) and determine the local decision boundaries among related subspaces. A decision boundary defined in the input space can be considered as being composed of several decision boundaries defined in subspaces that form the entire input space. For the decision boundaries defined in the subspaces, their nonlinearity becomes lower in comparison with the one being encountered when considering the entire input space. Through the weighted LSE estimation instead of using the LSE estimation method, the connections of several NNs can be estimated without interfering with each other. After estimating the weights, the decision boundaries defined in the related subspaces are merged to a single decision boundary by using fuzzy ensemble technique. Several machine learning datasets and one real world application dataset are used to evaluate and validate the proposed fuzzy ensemble classifier. Based on the experimental results, the proposed classifier shows better classification performance when compared with the performance of some selected classifiers.

Utilizing granular computing to enhance artificial neural network architecture, a new type of network emerges-the granular neural network (GNN).GNNs offer distinct advantages over their traditional counterparts: The ability to process both numerical and granular data, leading to improved interpretability.This paper proposes a novel design method for constructing GNNs, drawing inspiration from existing interval-valued neural networks built upon NNNs.However, unlike the proposed algorithm in this work, which employs interval values or triangular fuzzy numbers for connections, existing methods rely on a pre-defined numerical network.This new method utilizes a uniform distribution of information granularity to granulate connections with unknown parameters, resulting in independent GNN structures.To quantify the granularity output of the network, the product of two common performance indices is adopted: The coverage of numerical data and the specificity of information granules.Optimizing this combined performance index helps determine the optimal parameters for the network.Finally, the paper presents the complete model construction and validates its feasibility through experiments on datasets from the UCI Machine Learning Repository.The results demonstrate the proposed algorithm's effectiveness and promising performance.