Granular Computing: Perspectives and Challenges

Granular computing is a problem solving paradigm based on information granules, which are conceptual entities derived through a granulation process. Solving a complex problem, via a granular computing approach, means splitting the problem into information granules and handling each granule as a whole. This leads to a multi-level view of information granulation, which permeates human reasoning and has a significant impact in any field involving both human-oriented and machine-oriented problem solving. In this chapter we examine a view of granular computing as a paradigm of human-inspired problem solving and information processing with multiple levels of granularity, with special focus on fuzzy information granulation. To support the importance of granulation with multiple levels, we present a multi-level approach for extracting well-defined and semantically sound fuzzy information granules from numerical data.

Based on formal concept analysis we propose a novel lattice visualization system for huge image databases as a realization of the important paradigm of human-centered information processing based on granular computing. From a given cross table of objects (images) and attributes (image features) the proposed system first constructs a concept lattice. Then the Hasse diagram of this lattice is visualized. The information granules in the proposed system correspond to the elements of the concept lattice. All the important components of granular computing are shown to be present in the proposed system, such as: abstraction of data, derivation of knowledge and empirical verification of the abstraction. Since formal concept analysis generates an order relation, we obtain a hierarchical structure of concepts. This structure is shown to be also strongly related to the granular computing, since this is how the lattice visualization system implements the zoom in and zoom out capability of granular computing systems. Using the proposed system, a user can freely analyze the perspective and detailed structure of a large image database in the setting of granular computing. Furthermore, through an interaction function, the potential user can adjust the quantization of features, being able in this way, to select the attributes which allow him to obtain a suitable concept lattice. Therefore, the proposed system can be regarded as a promising human-centric information processing algorithm, based on granular computing.KeywordsImage DatabaseComplete LatticeConcept LatticeVisualization SystemFormal Concept AnalysisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Granular computing is an emerging computing paradigm of information processing. It concerns the processing of complex information entities, called 'information granules', which appear in the process of data abstraction and derivation of knowledge from information. The granular computing paradigm has been applied to many applications and we will address the applications of granular computing in the area of privacy-preserving data mining. We will use privacy-preserving association rule mining, privacy-preserving k-nearest neighbour classification and privacy-preserving support vector machine classification to illustrate how the paradigm of granular computing has been applied.

Granular computing is an umbrella term to cover a series of theories, methodologies, techniques, and tools that make use of information granules in complex problem solving. Rough sets, as one of the main concrete models of granular computing, has attracted considerable attention and has been successfully applied to numerous kinds of fields. To show the basic ideas and principles of granular computing from the perspective of rough sets, the main models, uncertainty measures and applications of rough sets are surveyed in the paper.

This book is about granular computing, its fundamentals, methodologies, algorithms and applications. In a nuthshell, granular computing, as the name itself stipulates, deals with representing information in the form of some aggregates (embracing a number of individual entitites) and their processing. Information granules are everywhere. They are central to processes of abstraction guiding our intellectual pursuits. Without any exaggeration one can state that processing at the level of information granules is a predominant feature of knowledge-intensive systems. This chapter serves as a concise and gentle introduction to the subject. First, we introduce the notion of information granularity through a discussion of several illustrative examples that come from commonly visible and representative areas of engineering and science. Second, we elaborate on a number of formal models of information granules and their processing. Along this line comes a discussion on the conceptual and algorithmic aspects of information granules such as their granularity, usefulness, communication and interoperability between various platforms of granular computing.

Granular Computing is a new method of simulating human thinking and solving complex problems in the current field of computational intelligence research.It covers theories, methods and techniques of all relevant granularity, which is the powerful tool of studying complex problem solving, massive data mining and fuzzy information processing and so on.The main idea of granular computing approach is to solve problems at different levels of granularity, reflecting the intelligence in human problem solving process to a great extent.With the deepening of granular computing research work, different theoretical models of granular computing have been acquired from different angles, the major granular computing model includes theoretical model of fuzzy set, theory model of rough set and theory model of commercial space.This paper analyzes the theoretical basis of existing granular computing model and centers on granular computing theory study in the hierarchical order, and has conducted systematic analysis and research for the construction of hierarchical knowledge granularity space, the uncertainty of hierarchical knowledge granularity spatial structure, the uncertainty of rough sets under hierarchical knowledge granular space and knowledge acquisition based on hierarchical knowledge granularity and so on.

As an emerging conceptual and computing paradigm of information processing, granular computing has received much attention recently. Many models and methods of granular computing have been proposed and studied. Among them was the granular computing model using information tables. In this paper, we shall demonstrate the application of this granular computing model for the study of a specific data mining problem - outlier detection. Within the granular computing model using information tables, this paper proposes a novel definition of outliers - GrC (granular computing)-based outliers. An algorithm to find such outliers is also given. And the effectiveness of GrC-based method for outlier detection is demonstrated on three publicly available databases.

Granular computing is to imitate human’s multi-granular computing strategy to problem solving in order to endow computers with the same capability. Its final goal is to reduce the computational complexity. To the end, based on the simplicity principle the problem at hand should be represented as simpler as possible. From structural information theory, it’s known that if a problem is represented at different granularities, the hierarchical description of the problem will be a simpler one. The simpler the representation the lower the computational complexity of problem solving should be. We presented a quotient space theory to multi-granular computing. Based on the theory a problem represented by quotient spaces will have a hierarchical structure. Therefore, the quotient space based multi-granular computing can reduce the computational complexity in problem solving. In the talk, we’ll discuss how the hierarchical representation can reduce the computational complexity in problem solving by using some examples.

Granular Computing (GrC) is an umbrella term to cover any theory, methodology, technique and tool that makes usage of granules in the complex problem solving and provides an effective method for massive data-mining in huge data warehouse system. This paper presents a time granularity model firstly and then put the time granularity in applications which can reflect Granular Computing (GrC) mining at different times levels.

Granular computing, an emerging information processing paradigm transforming complex data into information granules at different scales so that different features and regularities can be revealed, offers an essential linkage between big data and decision making. By using innovative technologies of granular computing that transforms big data collections into information granules, we would be at position of recognizing and exploiting the meaningful pieces of knowledge present in data, and produce sound, and practically supported decisions. In this study, we first summarize a general scheme of big data–granular computing–decision making and then present a case study where we detect the important traffic event information by collecting and analyzing social media data, and transform them into probabilistic information granules that can be used for urban routing navigation. We propose a robust fastest path optimization model to incorporate the impact of traffic events and generate the optimal routing strategy. Real-life experiments are carried out in regional Chaoyang District, Beijing, as well as the backbone roadway network of Beijing, which illustrate the effectiveness of our proposed big data-driven decision-making method. Our study provides new evidence demonstrating that big data can be efficiently used to enhance decisions and granular computing with this regard. The concept of the proposed scheme can be easily extended for decision-making modeling in other domains.

The steadily increasing volume of road traffic has resulted in many safety problems. Road safety performance indicators may contribute to better understand current safety conditions and monitor the effect of policy interventions. A composite road safety performance indicator is desired to reduce the dimensions of selected risk factors. The essential step for constructing such a composite indicator is to assign a suitable weight to each indicator. However, no agreement on weighting and aggregation in the composite indicator literature has been reached so far. Granular computing is an emerging computing paradigm of information processing that makes use of granules in problem solving. Rough set theory is considered as one of the leading special cases of granular computing approaches. In this article, a new weighting approach based on rough set theory and granular computing is introduced for road safety indicator analysis. The proposed method is applied to a real case study of 21 European countries of which only the class information (not the real values) on all indicators is used to calculate the weights. Experimental evaluation shows that it is an efficient approach to combine individual road safety performance indicators into a composite one.

Recently, the rough set and fuzzy set theory have generated a great deal of interest among more and more researchers. Granular computing (GrC) is an emerging computing paradigm of information processing and an approach for knowledge representation and data mining. The purpose of granular computing is to seek for an approximation scheme which can effectively solve a complex problem at a certain level of granulation. This issue on the theory and application about rough set, fuzzy logic and granular computing, most of which are very meticulously performed reviews of the available current literature. Four models of fuzzy or rough sets that are leading to a greater understanding of rough sets and fuzzy sets are discussed. These include multigranulation T-fuzzy rough sets, the so called approximation set of the interval set, the generalized interval-valued fuzzy rough set, and the δ-cut decision-theoretic rough set. Based on a kernelized information entropy model, an application on the fault detection and diagnosis for gas turbines is presented. The methods for reductions and their relevant algorithms are addressed in two manuscripts. Y. Zhang studies the distribution reduction in the inconsistent ordered information systems and further provides its algorithm. H. Ju et al. firstly give the model of δ-cut decision-theoretic rough set and then investigate the attribute reductions in this new decision-theoretic rough set model. From the view of GrC, the optimistic multigranulation T-fuzzy rough set model was established based on multiple granulations under T-fuzzy approximation space by W. Xu. The manuscript of W. Li et al. improves the optimistic multigranulation T-fuzzy rough set deeply by investigating some further properties. And the relationships between multigranulation and classical T-fuzzy rough sets have been studied carefully. The interval set is a special fuzzy set, which describes uncertainty of an uncertain concept with its two crisp boundaries. Q. Zhang et al. review the similarity degrees between an interval-valued set and its two approximations and propose disadvantages of using upper approximation set or lower approximation as approximation sets of the uncertain set and present a new method for looking for a better approximation set of the interval set. T. Xue et al. also construct a novel model of the generalized fuzzy rough set under interval-valued fuzzy relation. The aim of this special issue is to encourage researchers in related areas to discuss and communicate the latest advancements of rough set, fuzzy logic, and GrC, which covers both theoretical and practical results. Xibei Yang Weihua Xu Yanhong She

Granular computing is an emerging computing paradigm of information processing. It concerns the processing of complex information entities, called ldquoinformation granulesrdquo, which appear in the process of data abstraction and derivation of knowledge from information. The granular computing paradigm has been applied to many applications and we will address the application of granular computing in privacy-preserving data mining. We will use privacy-preserving association rule mining and privacy-preserving k-nearest neighbor classification to illustrate how the paradigm of granular computing has been applied.

Relational granulation method based on Quotient Space Theory for maximum flow problem

Granular computing is the emerging technique which performs data processing through making multiple levels of descriptions. Each level of description is expressed through granules or chunks of data also defined as information granules. The granule, the granule structure, and the granule layer are the heart of granular computing. Ontologies are vital information archives. On all disciplines of science and technology, ontologies are developed according to the requirements. Hence, the huge number of ontologies is available in the concerned domain which creates information duplication and storage problem. Merging of existing ontologies overcomes these issues. There are many merging approaches available. The existing approaches do not use granular computing for merging the ontologies. The proposed approach employs granular computing for merging the existing domain ontologies, thereby unifying multiple domain ontologies into a single representative domain ontology. For that, this research work proposes the following four granular computing processes, namely, association, isolation, purification, and reduction which can be applied over a group of similar nodes in the ontologies thereby unifying them. The proposed method achieves the ontology merging by performing two phases, namely similarity calculation phase and granular computing phase. The similarity calculation phase identifies the inter-label similarity between the labels of ontologies and computes the relevant group of nodes. Subsequently, granular computing applies association, isolation, purification, and reduction over a group of relevant nodes. The proposed approach is validated using the film industry and transportation domain ontologies and compared against its counterpart hybrid semantic similarity measure (HSSM). The results concluded that the proposed approach outperforms HSSM.