Granular Computing

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.

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...

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 ...

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.

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.

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.

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.

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.