Principles Of Granular Computing Research Articles

Tri-granularity attribute reduction of three-way concept lattices

A real-world dataset often generates a huge concept lattice that may be difficult to understand and impractical to use. The principle of granular computing is that we can understand and use a complex whole at multiple levels of granularity. In light of this, we propose a unified tri-granularity model of various types of concept lattices, which allows us to examine a huge concept lattice at three levels of granularity (i.e., the elementary granularity, local granularity and global granularity). Attribute reduction plays a fundamental role in three-way concept analysis, it simplifies the expression of three-way concepts and thus contributes to a better perception of the knowledge in three-way concept lattices. The tri-granularity model suggests an opportunity to investigate the tri-granularity attribute reduction of three-way concept lattices. The existing research on attribute reduction works at the global granularity but pays little attention to the local granularity, or, even less, to the elementary granularity. Driven by these issues, we supply definitions and methods of local granularity and elementary granularity attribute reduction of three-way concept lattices. These newly proposed two levels of attribute reduction with the existing global granularity attribute reduction together provide a framework for the tri-granularity attribute reduction of three-way concept lattices. We further analyze the relationships among the three levels of attribute reduction. Moreover, the efficacy of our suggested approach is illustrated by an example via the trisections induced by three-way concepts. Finally, we design two tri-granularity attribute reduction algorithms whose effectiveness is further examined by numerical experiments.

Long-term learning for type-2 neural-fuzzy systems

The development of a new long-term learning framework for interval-valued neural-fuzzy systems is presented for the first time in this article. The need for such a framework is twofold: to address continuous batch learning of data sets, and to take advantage the extra degree of freedom that type-2 Fuzzy Logic systems offer for better model predictive ability. The presented long-term learning framework uses principles of granular computing (GrC) to capture information/knowledge from raw data in the form of interval-valued sets in order to build a computational mechanism that has the ability to adapt to new information in an additive and long-term learning fashion. The latter, is to accommodate new input–output mappings and new classes of data without significantly disturbing existing input–output mappings, therefore maintaining existing performance while creating and integrating new knowledge (rules). This is achieved via an iterative algorithmic process, which involves a two-step operation: iterative rule-base growth (capturing new knowledge) and iterative rule-base pruning (removing redundant knowledge) for type-2 rules. The two-step operation helps create a growing, but sustainable model structure. The performance of the proposed system is demonstrated using a number of well-known non-linear benchmark functions as well as a highly nonlinear multivariate real industrial case study. Simulation results show that the performance of the original model structure is maintained and it is comparable to the updated model's performance following the incremental learning routine. The study is concluded by evaluating the performance of the proposed framework in frequent and consecutive model updates where the balance between model accuracy and complexity is further assessed.

A novel granular approach for detecting dynamic online communities in social network

The great surge in the research of community discovery in complex network is going on due to its challenging aspects. Dynamicity and overlapping nature are among the common characteristics of these networks which are the main focus of this paper. In this research, we attempt to approximate the granular human-inspired viewpoints of the networks. This is especially helpful when making decisions with partial knowledge. In line with the principle of granular computing, in which precision is avoided, we define the micro- and macrogranules in two levels of nodes and communities, respectively. The proposed algorithm takes microgranules as input and outputs meaningful communities in rough macrocommunity form. For this purpose, the microgranules are drawn toward each other based on a new rough similarity measure defined in this paper. As a result, the structure of communities is revealed and adapted over time, according to the interactions observed in the network, and the number of communities is extracted automatically. The proposed model can deal with both the low and the sharp changes in the network. The algorithm is evaluated in multiple dynamic datasets and the results confirm the superiority of the proposed algorithm in various measures and scenarios.

Unified granular neural networks for pattern classification

Motivation in the development of granular neural network (GNN) with the principle of granular computing (GrC) is to obtain possible degree of transparency in the network architecture and its operational steps, which are bottleneck for conventional neural network (NN). In addition, GNN provides improved performance and at the same time poses less computational burden compared to conventional NN and fuzzy NN (FNN). Topologically, the nodes of different layers of FNNs are fully connected whereas it is partial in case of GNNs. Further, the architectures of GNN is determined based on the extracted rules from the domain information. However, selection of relevant rules for GNN is a tedious task. To mitigate this, the present paper aims to develop a pattern classification model in the framework of unification of GNNs and tries to avoid the searching of optimum number of rules and the best combination of rules. The unified model thus works with a set of different rules-based GNNs and derives the final decision from the individual GNN. Each of these GNNs takes the class-supportive fuzzy granulated features of the input in order to preserve the feature-wise belonging information to different classes. These granulated features provide improved class discriminatory information for the classification of data sets with ill-defined and overlapping class boundaries. The proposed model thus explores mutually the advantages of class-supportive fuzzy granulation of features, informative rules-based GNNs and unification of GNNs. Superiority of the model to similar other methods are justified in terms of various performance measurement indexes using different benchmark data sets including remote sensing imagery.

Hierarchical Architectures of Fuzzy Models: From Type-1 fuzzy sets to Information Granules of Higher Type

Complex phenomena are perceived from different perspectives, diversified conceptual points of view and at various levels of granularity. Symbolic and sub-symbolic processing becomes an inherently visible computing practice. Distributed nature of perception becomes reflected in topologies of multi-agent systems. All of these facets challenge the well-established paradigms of system modeling including fuzzy models and neural networks. In spite of the diversity of existing architectures and underlying algorithms, a vast majority of fuzzy models adheres to the surprisingly homogeneous principles of Granular Computing, that are associated with the processing of granular information. In this study, being cognizant of this underpinning, we concentrate on the architectures and fundamentals supporting the reconciliation and characterization of a family of fuzzy models aimed at the representation of the same system (phenomenon) from different cognitive perspectives. The variety of points of view is reflected in dif...