Granular Computing

We discuss information granule calculi as a basis of granular computing. They are defined by constructs like information granules, basic relations of inclusion and closeness between information granules as well as operations on them. The exact interpretation between granule languages of different information sources (agents) often does not exist. Hence (rough) inclusion and closeness of granules are considered instead of their equality. Examples of all the basic constructs of information granule calculi are presented. The construction of more complex information granules is described by expressions called terms. We discuss the synthesis problem of robust terms, i.e., descriptions of information granules, satisfying a given specification in a satisfactory degree. We also present a method for synthesis of information granules represented by robust terms (approximate schemes of reasoning) by means of decomposition of specifications for such granules. The discussed problems of granular computing are of special importance for many applications, in particular related to spatial reasoning as well as to knowledge discovery and data mining.

Community detection in a social network is a well-known problem that has been studied in computer science since early 2000. The algorithms available in the literature mainly follow two strategies, one, which allows a node to be a part of multiple communities with equal membership, and the second considers a disjoint partition of the whole network where a node belongs to only one community. In this paper, we proposed a novel community detection algorithm which identifies fuzzy-rough communities where a node can be a part of many groups with different memberships of their association. The algorithm runs on a new framework of social network representation based on fuzzy granular theory. A new index viz. normalized fuzzy mutual information, to quantify the goodness of detected communities is used. Experimental results on benchmark data show the superiority of the proposed algorithm compared to other well known methods, particularly when the network contains overlapping communities.

Rule learning is one of the most popular types of machine-learning approaches, which typically follow two main strategies: 'divide and conquer' and 'separate and conquer'. The former strategy is aimed at induction of rules in the form of a decision tree, whereas the latter one is aimed at direct induction of if-then rules. Due to the case that the divide and conquer strategy could result in the replicated sub-tree problem, which not only leads to overfitting but also increases the computational complexity in classifying unseen instances, researchers have thus been motivated to develop rule learning approaches through the separate and conquer strategy. In this paper, we focus on investigation of the Prism algorithm, since it is a representative one that follows the separate and conquer strategy, and is aimed at learning a set of rules for each class in the setting of granular computing, where each class (referred to as target class) is viewed as a granule. The Prism algorithm shows highly comparable performance to the most popular algorithms, such as ID3 and C4.5, which follow the divide and conquer strategy. However, due to the need to learn a rule set for each class, Prism usually produces very complex rule-based classifiers. In real applications, there are many problems that involve one target class only, so it is not necessary to learn a rule set for each class, i.e., only a set of rules for the target class needs to be learned and a default rule is used to indicate the case of non-target classes. To address the above issues of Prism, we propose a new version of the algorithm referred to as PrismSTC, where 'STC' stands for 'single target class'. Our experimental results show that PrismSTC leads to production of simpler rule-based classifiers without loss of accuracy in comparison with Prism. PrismSTC also demonstrates sufficiently good performance comparing with C4.5.

Quality factors namely testability, reliability, and maintainability are considered vulnerable to software complexity. Analyzing complexity of code is difficult though. Many techniques have been invented, including control flow graph (CFG) to aid program complexity analysis. However, the representation of code with 'web' structures exploited in CFG incurs some difficulty to human comprehension. Referring to Granular computing recently emerging from cognitive theories, this research thus proposes a novel approach to representing source code with "granular hierarchical structures". Instead of representing a program with 'web', the method uses multiple 'trees' to promisingly obtain more understanding during source code analysis. Preliminary experiments showed that representing source code with granular hierarchical structures gained more competent analysis of program complexity. The results were evaluated by the invented complexity measure called SCIM that satisfies more "basic needs of good software measures", compared to McCabe's Cyclomatic complexity derived from control flow graph.

Information granules are complex entities that arise in the process of abstraction of data and derivation of knowledge. The automatic generation of information granules from data is an important task, since it gives to machines the ability of acquiring knowledge that can be communicated to users. For this purpose, knowledge acquisition should provide for fuzzy information granules that can be naturally labelled by linguistic terms, i.e. symbols that belong to the natural language. Information granules of this type are called interpretable. However, interpretability cannot be guaranteed until a set of constraints is imposed on the granulation process. In literature, several interpretability constraints have been proposed, but, due to the subjective interpretation of interpretability, there is no agreement on which constraints should be adopted. This survey is an attempt to provide for a complete presentation of interpretability constraints adopted in literature with the following objectives: (i) to give a homogeneous description of all interpretability constraints; (ii) to provide for a critical review of such constraints; (iii) to identify potentially different meanings of interpretability. Hopefully, this survey may serve as a guidance for designing interpretable fuzzy models as well as for identifying new methods of interpretable information granulation.

This book contains thirteen chapters. There are (1) Preliminary, (2) Formal Context Based on Pictorial Diagram, (3) Partially-Ordered Attribute Diagram, (4) Non-matrix Knowledge Reduction Method for Fuzzy Context, (5) Interval-Set-Based Concept Lattice, (6) Axiality Concept Lattice and Its Attribute Redction, (7) Representation of Special Ordered Structure Based on FCA, (8) Decision Logic of Concept Lattice, (9) Attribute Reduction in Intuitionistic Fuzzy Generalized Consistent Decision Context, (10) Two-way Learning Based on FCA in Fuzzy Datasets, (11) Rule comparison Between Conept Lattice and Multi-granulation Rough Set, (12) Attribute Topology and Its Application, and (13) Triadic Concept Analysis.

This paper investigates a novel graph embedding procedure based on simplicial complexes. Inherited from algebraic topology, simplicial complexes are collections of increasing-order simplices (e.g., points, lines, triangles, tetrahedrons) which can be interpreted as possibly meaningful substructures (i.e., information granules) on the top of which an embedding space can be built by means of symbolic histograms. In the embedding space, any Euclidean pattern recognition system can be used, possibly equipped with feature selection capabilities in order to select the most informative symbols. The selected symbols can be analysed by field-experts in order to extract further knowledge about the process to be modelled by the learning system, hence the proposed modelling strategy can be considered as a grey-box. The proposed embedding has been tested on thirty benchmark datasets for graph classification and, further, we propose two real-world applications, namely predicting proteins’ enzymat...

Attribute reduction of an information system is a key problem in rough set theory and its applications. Using computational intelligence (CI) tools to solve such problems has recently fascinated many researchers. CI tools are practical and robust for many real-world problems, and they are rapidly developed nowadays. However, some classes of CI tools, like memory-based heuristics, have not been involved in solving information systems and data mining applications like other well-known CI tools of evolutionary computing and neural networks. In this paper, we consider a memory-based heuristic of tabu search to solve the attribute reduction problem in rough set theory. The proposed method, called tabu search attribute reduction (TSAR), shows promising and competitive performance compared with some other CI tools in terms of solution qualities. Moreover, TSAR shows a superior performance in saving the computational costs.

Linguistic summarization is a data mining or knowledge discovery approach to extract patterns from databases. In this report linguistic summarization is used to extract IF-THEN rules from databases, an approach that has not been studied by others. Several quality measures for such summaries are defined and computed. Experiments on four datasets verify the effectiveness of our approach. The rules generated from summarization can be added to a knowledge base for better understanding of the data, or be used in Perceptual Reasoning to infer the outputs for new scenarios.

The basic contribution of this paper is the presentation of two methods that can be used to design a practical software change classification system based on data mining methods from rough set theory. These methods incorporate recent advances in rough set theory related to coping with the uncertainty in making change decisions either during software development or during post-deployment of a software system. Two well-known software engineering data sets have been used as means of benchmarking the proposed classification methods, and also to facilitate comparison with other published studies on the same data sets. Two technologies in computation intelligence (CI) are used in the design of the software change classification systems described in this paper, namely, rough sets (a granular computing technology) and genetic algorithms. Using 10-fold cross validated paired t-test, this paper also compares the rough set classification learning method with the Waikato Environment for Knowledge Analysis (WEKA) classification learning method. The contribution of this paper is the presentation of two models for software change classification based on two CI technologies. She has published numerous papers on rough neurocomputing, rough control and application of choquet integral in software cost and quality estimation. Her current research interests are in the use of rough set methods in approximate reasoning and in software engineering.

This book constitutes the refereed proceedings of the 12th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, RSFDGrC 2009, held in Delhi, India in December 2009 in conjunction with the Third International Conference on Pattern Recognition and Machine Intelligence, PReMI 2009. RSFDGrC 2009 is the core component of a broader Rough Set Year in India initiative, RSIndia09. The 56 revised full papers presented together with 6 invited papers and a report on the Rough Set Year in ...

Granular computing has been applied in many fields to solve problems and describe spaces at different granularity and hierarchies. This paper proposes a rule generation approach based on granular computing using rough mereology. The proposed approach generates a single rule granule from granular space in each step instead of selecting a suitable attribute according to some measure and improve the performance of rule granule generation. Rules are generated by using voting strategy based on weights computed by means of rough inclusions induced from residual implications of continuous t-norm. Experimental results obtained show that the overall accuracy rate average of dataset is 64.7%, which is higher than other approaches applying decision tree algorithms. Also, the resulted average rule length is 2.25, which is less than average rule length generated using decision tree algorithms.

Cognitive concept learning is to learn concepts from a given clue by simulating human thought processes including perception, attention and thinking. In recent years, it has attracted much attention from the communities of formal concept analysis, cognitive computing and granular computing. However, the classical cognitive concept learning approaches are not suitable for incomplete information. Motivated by this problem, this study mainly focuses on cognitive concept learning from incomplete information. Specifically, we put forward a pair of approximate cognitive operators to derive concepts from incomplete information. Then, we propose an approximate cognitive computing system to perform the transformation between granular concepts as incomplete information is updated periodically. Moreover, cognitive processes are simulated based on three types of similarities. Finally, numerical experiments are conducted to evaluate the proposed cognitive concept learning methods.

This work presents a granular K Nearest Neighbor, or grKNN for short, classifier in the metric lattice of Intervals' Numbers (INs). An IN here represents a population of numeric data samples. We detail how the grKNN classifier can be parameterized towards optimizing it. The capacity of a preliminary grKNN classifier is demonstrated, comparatively, in four benchmark classification problems. The far-reaching potential of the proposed classification scheme is discussed.

Social network data has been modeled with several approaches, including Sociogram and Sociomatrices, which are popular and comprehensive. Similar to these we have developed here a novel modeling technique based on granular computing theory and fuzzy neighborhood systems, which provides a uniform framework to represent social networks. In this model, a social network is represented with a collection of granules. Fuzzy sets are used for defining the granules. The model is named Fuzzy Granular Social Network (FGSN). Familiar measures of networks viz. degree, betweenness, embeddedness and clustering coefficient are redefined in the context of this new framework. Two measures, namely, entropy of FGSN and energy of granules are defined to quantify the uncertainty involved in FGSN arising from fuzziness in the relationships of actors.Experimental results demonstrate the applicability of the model in two well known problems of social networks, namely, target set selection and community detection with comparative studies.

Diamond granular computing segmentation algorithm is presented to solve the low segmentation speed of color image segmentation based on clustering method. For a color image, the RGB feature of each pixel point is represented as an atomic diamond granule with the center RGB and radii 0, the merging operator between two diamond granules is designed to obtain the granule with greater granularity, the granularity threshold is set to merge two diamond granules and obtain the diamond granule set including granules with different granularities. The RGB of pixels belonging to the same diamond granule is replaced by the RGB of the diamond granule’s center. The experimental results show that the diamond granular computing segmentation algorithm is stable and reduces the segmentation time compared with Kmeans and FCM segmentation algorithms.

Professor Degang Chen, professor Weihua Xu, and professor Jinhai Li organized a special issue entitled "Granular Computing in Machine Learning" in the Granular Computing journal (http://www.springer.com/engineering/computational+intelligence+and+complexity/journal/41066). We sincerely invited you to submit excellent wrok to our special issue. Thank you in advance.

One of the major challenges of the modern bioinformatics research is to integrate biological pathway data to understand the inner working of the cell. Various pathway data sources are often structured differently and employ algorithms for analysis and integration. Each has a specific motivation for integration that may be suitable only for a particular type of pathway like metabolic pathway or protein protein interactions. Additionally, with the documentation associated with biological pathway data sources, one needs to understand the database schemas used to store data in each source system, and translate among the schemas in order to exchange information between them. The authenticity of a data source may be subjective as many of them are not independent but derived and data sources often contain similar or overlapping data elements but use conflicting data definitions. There is often a need for user-friendly tools and interfaces to transform bioinformatics data from one database schema to another to discover correlated data among many databases, regardless of the structure of the databases. Most importantly, there are no standards set up for developing biological pathway source and integration. The integration mechanisms may not register important metadata like, copies of input files and time of integration along with the integrated output file.

A new method for finding fuzzy information granules from multivariate data through a gravitational inspired clustering algorithm is proposed in this paper. The proposed algorithm incorporates the theory of granular computing, which adapts the cluster size with respect to the context of the given data. Via an inspiration in Newton's law of universal gravitation, both conditions of clustering similar data and adapting to the size of each granule are achieved. This paper compares the Fuzzy Granular Gravitational Clustering Algorithm (FGGCA) against other clustering techniques on two grounds: classification accuracy, and clustering validity indices, e.g. Rand, FM, Davies-Bouldin, Dunn, Homogeneity, and Separation. The FGGCA is tested with multiple benchmark classification datasets, such as Iris, Wine, Seeds, and Glass identification.

In this paper we propose a method to build similarity relations into extended Rough Set Theory. Similarity is estimated using ideas from Granular computing and Case-base reasoning. A new measure is introduced in order to compute the quality of the similarity relation. This work presents a study of a case of a similarity relation based on a global similarity function between two objects, this function includes the weights for each feature and local functions to calculate how the values of a given feature are similar. This approach was proved in the function approximation problem. Promissory results are obtained in several experiments.

Concrete models of GrC under specific contexts have been proposed over the years. Rough set theory is perhaps one of the most advanced approaches that popularizes GrC [9,. It was originally proposed by Pawlak as a formal tool for modelling and processing incomplete information. The basic structure of Pawlak's rough set theory is an approximation space consisting of a universe of discourse and an equivalence relation imposed on it. The equivalence relation groups together entities which are in some sense indiscernible or similar, called equivalence classes. Therefore equivalence classes are the basic building blocks for the representation and approximation of any subset of the universe of discourse. Based on the approximation space, the notions of lower and upper approximation operators can be constructed. Using the lower and upper approximations, knowledge hidden in information tables may be unravelled and expressed in the form of decision rules.

This paper considers anomaly network traffic detection using different network feature subsets. Fuzzy c-means vector quantization is used to train network attack models and the minimum distortion rule is applied to detect network attacks. We also demonstrate the effectiveness and ineffectiveness in finding anomalies by looking at the network data alone. Experiments performed on the KDD CUP 1999 dataset show that time based traffic features in the last two second time window should be selected to obtain highest detection rates.

In the plethora of conceptual and algorithmic developments supporting data analytics and system modeling, humancentric pursuits assume a particular position owing to ways they emphasize and realize interaction between users and the data. We advocate that the level of abstraction, which can be flexibly adjusted, is conveniently realized through Granular Computing. Granular Computing is concerned with the development and processing information granules-formal entities which facilitate a way of organizing knowledge about the available data and relationships existing there. This study identifies the principles of Granular Computing, shows how information granules are constructed and subsequently used in describing relationships present among the data.

Observing the world and finding trends and relations among the variables of interest is an important and common learning activity. In this paper we apply TETRAD, a program that uses Bayesian networks to discover causal rules, and C4.5, which creates decision trees, to the problem of discovering relations among a set of variables in the controlled environment of an Artificial Life simulator. All data in this environment are generated by a single entity over time. The rules in the domain are known, so we are able to assess the effectiveness of each method. The agent’s sensings of its environment and its own actions are saved in data records over time. We first compare TETRAD and C4.5 in discovering the relations between variables in a single record. We next attempt to find temporal relations among the variables of consecutive records. Since both these programs disregard the passage of time among the records, we introduce the flattening operation as a way to span time and bring the variables of interest together in a new single record. We observe that flattening allows C4.5 to discover relations among variables over time, while it does not improve TETRAD’s output.

Granular computing as a paradigm is an area frequently studied within the Approximate Reasoning paradigm. Proposed by L. A.Zadeh granular computing has been studied within fuzzy as well as rough set approaches to uncertainty. It is manifest that both theories are immanently related to granulation as fuzzy set theory begins with fuzzy membership functions whose inverse images are prototype granules whereas rough set theory starts with indiscernibility relations whose classes are prototype, or, elementary granules. Many authors have devoted their works to analysis of granulation of knowledge, definitions of granules, methods for combining (fusing) granules into larger objects, applications of granular structures, see, quoted in references works by A. Skowron, T.Y. Lin, Y.Y.Yao, L.Polkowski and others. In this work, the emphasis is laid on granular decision (data) systems: they are introduced, methods of their construction with examples are pointed to, and applications are exhibited; those applications are founded on the basic although often implicit principle of data mining, viz., once a plausible for given data similarity measure is found, objects satisfactorily similar should reveal sufficiently close (or, for that matter identical) class values. In this work, this principle is applied to granules, following the idea presented by L.Polkowski at 2005, 2006 IEEE GrC conferences, that granules built on basis of a similarity relation from a given decision system should consists of objects similar to such a degree that averaging them would lead to new objects which together would constitute a new decision system preserving to a high degree knowledge represented by the original decision system. As knowledge in rough set theory is meant as the classification ability, it seems reasonable to test knowledge content with classifiers as classifier accuracy. This informal idea is tested in this work with some specific tools for granule construction, granular system building, and some well-tested classifiers known in literature for a few data sets from the UCI repository. In the following sections we outline: basic ideas of rough computing, granulation of knowledge, the idea of a granular decision system and we include the results of exemplary tests with real data.

Holon is a powerful metaphor which captures the recursive structure of biological systems and the organization of their decision processes arranged at various granularity abstraction levels. From a computational intelligence perspective, a holon can be conceived as a goal-oriented community of lower-level holons led by more specific targets. Sub-holons co-operate on sub-problems that represent the source problem at a lower knowledge abstraction level. Such a (recursive) hierarchical organization constitutes the so-called holarchy. Holonic thinking is hence particularly suited for complex and intelligent systems modeling: in particular, its success has been proved in the field of Intelligent Manufacturing. Nevertheless, albeit hierarchical and granular thinking are two fundamental prerequisites in Software Engineering, the use of holonic thinking as software paradigm is still flawing in the literature at the moment. In this regard, the paper introduces the concept of 'holonic granule' as a novel software building-block for modeling complex granular systems. Prospective applications of holonic granule-based software models are then commented with particular emphasis to industrial automation and environmental monitoring settings.

A granular neural Web-based stock prediction agent is developed using the granular neural network (GNN) that can discover fuzzy rules. Stock data sets are downloaded from www.yahoo.com website. These data sets are inserted into the database tables using a java program. Then, the GNN is trained using sample data for any stock. After learning from the past stock data, the GNN is able to use discover fuzzy rules to make future predictions. After doing simulations with six different stocks (msft, orcl, dow, csco, ibm, km), it is conclusive that the granular neural stock prediction agent is giving less average errors with large amount of past training data and high average errors in case of fewer amounts of past training data. Java Servlets, Java Script and jdbc are used. SQL is used as the back-end database. The performance of the GNN algorithm is compared with the performance of the BP algorithm by training the same set of data and predicting the future stock values. The average error of the GNN is less than that of BP algorithm.

A new sliding window scheme is introduced with multiple windows to form the protein data for SVM. Two new tertiary classifiers are introduced; one of them makes use of support vector machines as neurons in neural network architecture and the other tertiary classifier is a granular decision tree based on granular computing, decision tree and SVM. Binary classifier using multiple windows is compared with single window scheme. The accuracy levels of the new classifiers are better than most available techniques.

A topological space is a "space", where "near" makes sense; it is formally defined by the T opological N eighborhood System (TNS). Here, we explore the concept of "conflict" by the system of "Anti-TNS"; by that we mean a "mathematical structure" that consists of a set of "punctured" neighborhoods, namely, the center point p of all neighborhoods of TNS has been removed. "Conflicts" are important concepts in computer security. The primary results is the axiomatization of ATNS. The main results are surprising: The set of the axioms is the same as that of topological spaces. Similar results for pretopological spaces also are obtained.

lation, which form a basis of granular computing The key to granular computing (GrC) is to (GrC) [191. Basic ingredients of GrC are subsets, make use of granules in problem solving. Classi-classes, and clusters of a universe [13]. GrC is an fication is one of important problems in machine umbrella term which covers any theories, methodololearning and data mining. With view of granu-gies, techniques, and tools that make use of granules lar computing, this paper presents a classification in problem solving [17, 20]. approach to granules based on the variable pre-The topic of fuzzy information granulation was cision rough set (VPRS) model. An algorithm is first proposed and discussed by Zadeh [22] in 1979. proposed and a tree structure of granules is given. A general framework of GrC was presented by Zadeh [23] in the context of fuzzy set theory. On the other hand, many researchers investigated specific Keywords: and more concrete models of GrC. For example, Lin Granular computing; granules; variable preci-[4] and Yao [16] studied GrC using neighborhood sion rough sets.

概念是知识表示的基本认知单元,它由外延和内涵两部分构成.由于概念的外延与内涵可以相互诱导,所以概念的外延和内涵中一旦有一个被确定下来,那么这个概念也就随之确定.概念认知是将属于这一概念的特征属性筛选出来,同时把不属于这一概念的特征属性排除,即通过确定内涵的方式获得概念,它采用特定的认知方法来完成概念的识别.当前,概念认知正逐渐借鉴认知科学领域中的一些研究思想,不断地完善自身理论与方法.然而,现有的概念认知方法要求假定概念认知算子具有完全认知功能,但现实中由于个体认知的局限性往往会出现认知不完全的现象,在此情况下要对概念进行全面认知则需漫长等待,这意味着在时限约束条件下可能无法及时获取足够的概念信息.在认知科学领域,一般采取问题分解求解的策略解决此类问题,即根据当前的局部有限信息做出相应的快速决策,为阶段性认知提供有效的及时参考,是渐进式思维的一种认知模式.受此启发,本文提出概念的渐进式认知理论与方法,以处理不完全认知条件下的概念获取问题.具体地,提出概念渐进式认知的认知机理,其功能主要包括概念信息的增删改操作,以模拟一般的认知过程;针对线索为对象集、属性集以及对象集和属性集的三种不同情况,分别给出概念渐进式认知算法,并对它们的时间复杂度和空间复杂度进行分析.特别地,为了实现近似概念认知,设计乐观悲观两种信息融合策略,使得对于任意对象集和属性集为线索的概念认知至少获得一个上界概念.最后,数值实验表明概念渐进式认知算法的有效性.

In order to enrich the existing rule acquisition theory in formal decision contexts, this study puts forward three new types of rules: decision association rules, non-redundant decision association rules and simplest decision association rules. Then, we analyze the relationship among these three types of rules, and develop methods to acquire them from single-scale formal decision contexts. Some numerical experiments are also conducted to compare the performance of the method of acquiring the simplest decision association rules with that of the existing one of acquiring the non-redundant decision rules. Moreover, the new three types of rules are employed to introduce three types of consistencies in multi-scale formal decision contexts. In addition, the notion of an optimal scale is defined by each type of consistency, and how to select an optimal scale is investigated as well. Finally, two applications in smart city for the proposed rule acquisition and optimal scale selection methods are applied to smart city.

Information granules are complex entities that arise in the process of abstraction of data and derivation of knowledge. The automatic generation of information granules from data is an important task, since it gives to machines the ability of acquiring knowledge that can be communicated to users. For this purpose, knowledge acquisition should provide for fuzzy information granules that can be naturally labelled by linguistic terms, i.e. symbols that belong to the natural language. Information granules of this type are called interpretable. However, interpretability cannot be guaranteed until a set of constraints is imposed on the granulation process. In literature, several interpretability constraints have been proposed, but, due to the subjective interpretation of interpretability, there is no agreement on which constraints should be adopted. This survey is an attempt to provide for a complete presentation of interpretability constraints adopted in literature with the following objectives: (i) to give a homogeneous description of all interpretability constraints; (ii) to provide for a critical review of such constraints; (iii) to identify potentially different meanings of interpretability. Hopefully, this survey may serve as a guidance for designing interpretable fuzzy models as well as for identifying new methods of interpretable information granulation. 1 Roughly speaking, the level of granulation is the number of objects in the granule related to the total number of granules employed in a context. 2 Here, the term comprehensibility is used instead of interpretability. 3 Transparency can be related with ''white-box" models. 4586 C. Mencar, A.M. Fanelli / Information Sciences 178 (2008) 4585-4618

A rule based system is a special type of expert system, which typically consists of a set of if-then rules. Such rules can be used in the real world for both academic and practical purposes. In general, rule based systems are involved in knowledge discovery tasks for both purposes and predictive modelling tasks for the latter purpose. In the context of granular computing, each of the rules that make up a rule based system can be seen as a granule. This is due to the fact that granulation in general means decomposition of a whole into several parts. Similarly , each rule consists of a number of rule terms. From this point of view, each rule term can also be seen as a granule. As mentioned above, rule based systems can be used for the purpose of knowledge discovery, which means to extract information or knowledge discovered from data. Therefore, rules and rule terms that make up a rule based system are considered as information granules. This paper positions the research of rule based systems in the granular computing context, which explores ways of achieving advances in the former area through the novel use of theories and techniques in the latter area. In particular, this paper gives a certain perspective on how to use set theory for management of information granules for rules/rule terms and different types of computational logic for reduction of learning bias. The effectiveness is critically analyzed and discussed. Further directions of this research area are recommended towards achieving advances in rule based systems through the use of granular computing theories and techniques.

"Pre-determining locations and intensity of a seismic area is considered as a complicated disaster management problem.
All over the world scientists attempts to predict an impending earthquake with varied phenomena as seismicity patterns.
But still there exists uncertainty problem along with discovering knowledge from large and complex dataset that have significant influence on the final results. In this research granular computing algorithm employed to solve the problem of rule induction from existing dataset. As, this problem depends on various criteria, one of the most important challenges concerned is the existence of uncertainty regarding inconsistency in combining influencing criteria and extracting more consistent knowledge for the next predictions. To overcome this problem, this paper proposes a new approach for seismic risk knowledge discovery based on granular computing theory. One of the significant properties of this method is
induction of more compatible rules having zero inconsistency from existing databases. Furthermore, in this approach non-redundant covering rules will be extracted for consistent classification where one object maybe classified with two or more non-redundant rules. This paper illustrate the advantages of using granular computing to discovery of knowledge from dataset consist of the seismic risk properties of the area between 58° 24' E, 60° 24' E Longitude and 27° 45' N, 29° 25' N Latitude around occurred near Reygan (Kerman Province), South-East of Iran where a devastating earthquake
occurred."

The main goal of this paper is to integrate the relationships among rough set theory and topology. We introduce different closure operators by using binary relations. Using these operators, we construct generalized approximation operators in the theory of rough sets. In addition, new methods for generating different topologies from any binary relation (without using base or subbase) are provided. The main properties of suggested structures are investigated. Comparisons among the suggested operations and the previous works are constructed. The suggested methods depend, basically, on the “j-neighborhood space” that given by (Abd El-Monsef et al., Int J Granul Comput Rough Sets Intell Syst 3:292–305, 2014). These methods generate new granulation for rough sets. Finally, a practical example is introduced as a simple application for the suggested structures. We think that at the level of theoretical foundations and real-life implementations, the proposed approaches place emphasis on ties between rough sets, granular computing, and information discovery and data mining.