Rough-Granular Computing

Solving complex problems by multi-agent systems in distributed environments requires new approximate reasoning methods based on new computing paradigms. One such recently emerging computing paradigm is Granular Computing(GC). We discuss the Rough-Granular Computing(RGC) approach to modeling of computations in complex adaptive systems and multiagent systems as well as for approximate reasoning about the behavior of such systems. The RGC methods have been successfully applied for solving complex problems in areas such as identification of objects or behavioral patterns by autonomous systems, web mining, and sensor fusion.

Granular Computing for Data Analytics:A Manifesto of Human-Centric Computing

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.

Three Perspectives of Granular Computing

As an emerging field of study, granular computing has received much attention. Many models, frameworks, methods and techniques have been proposed and studied. It is perhaps the time to seek for a general and unified view so that fundamental issues can be examined and clarified.This paper examines granular computing from three perspectives.By viewing granular computing as a way of structured thinking,we focus on its philosophical foundations in modeling human perception of the reality.By viewing granular computing as a method of structured problem solving,we examine its theoretical and methodological foundations in solving a wide range of real-world problems.By viewing granular computing as a paradigm of information processing,we turn our attention to its more concrete techniques. The three perspectives together offer a holistic view of granular computing.

Granular Computing on Partitions, Coverings and Neighborhood Systems

Granular Computing on partitions(RST),coverings(GrCC) and neighborhood systems(LNS) are examined: (1) The order of generality is RST, GrCC, and then LNS. (2) The quotient structure: In RST, it is called quotient set. In GrCC, it is a simplical complex, called the nerve of the covering in combinatorial topology. For LNS, the structure has no known description. (3) The approximation space of RST is a topological space generated by a partition, called a clopen space. For LNS, it is a generalized/pretopological space which is more general than topological space. For GrCC,there are two possibilities. One is a special case of LNS,which is the topological space generated by the covering. There is another topological space, the topology generated by the finite intersections of the members of a covering The first one treats covering as a base, the second one as a subbase. (4) Knowledge representations in RST are symbol-valued systems. In GrCC, they are expression-valued systems. In LNS, they are multivalued system; reported in 1998 . (5) RST and GRCC representation theories are complete in the sense that granular models can be recaptured fully from the knowledge representations.

Two Classes of Models of Granular Computing

This paper reviews a class of important models of granular computing which are induced by equivalence relations,or by general binary relations,or by neighborhood systems,and propose a class of models of granular computing which are induced by coverings of the given universe.

Dominance-based rough set approach as a paradigm of knowledge discovery and granular computing

Dominance-based rough set approach(DRSA) permits representation and analysis of all phenomena involving monotonicity relationship between some measures or perceptions.DRSA has also some merits within granular computing,as it extends the paradigm of granular computing to ordered data,specifies a syntax and modality of information granules which are appropriate for dealing with ordered data,and enables computing with words and reasoning about ordered data.Granular computing with ordered data is a very general paradigm,because other modalities of information constraints,such as veristic,possibilistic and probabilistic modalities,have also to deal with ordered value sets(with qualifiers relative to grades of truth,possibility and probability),which gives DRSA a large area of applications.

A Granular Computing Model Based on Tolerance relation

Granular computing is a new intelligent computing theory based on partition of problem concepts. It is an important problem in Rough Set theory to process incomplete information systems directly. In this paper, a granular computing model based on tolerance relation for processing incomplete information systems is developed. Furthermore, a criteria condition for attribution necessity is proposed in this model.

Call for Paper of 2008 IEEE International Conference on Granular Computing Hangzhou,China,Aug.26～28,2008(http://www.cs.sjsu.edu/～grc/)Sponsored By IEEE Computational Intelligence Society

Contact Information:qliu_ncu@yahoo.com.cn,thu@cis.drexel.edu,and cc:grc@cs.sjsu.edu Keynote Speeches:Lotfi A.Zadeh(EE-Nobel Laureate,UC Berkeley,USA) Tsau Young Lin(GrC initiator,SJSU)

Editorial: Computational mechanics of granular materials

Most of granular materials are highly heteroge- neous, composed of voids and particles with different sizes and shapes. Geological matter, soil and clay in nature, geo-structure, concrete, etc. are practical ex- amples among them. From the microscopic view, a lo- cal region in the medium is occupied by particles with small but finite sizes and granular material is naturally modeled as an assembly of discrete particles in contacts On the other hand, the local region is identified with a material point in the overall structure and this discon- tinuous medium can then be represented by an effective continuum on the macroscopic level

Quotient space model based on algebraic structure

In the quotient space theory of granular computing,the universe structure is assumed to be a topology,therefore,its application is still limited.In this study,based on the quotient space model,the universe structure is assumed as an algebra instead of a topology.As to obtain the algebraic quotient operator,the granulation must be uniquely determined by a congruence relation,and all the congruence relations form a complete semi-order lattice,which is the theoretical basis of granularities ' completeness.When the given equivalence relation is not a congruence relation,it defines the concepts of upper quotient and lower quotient,and discusses some of their properties which demonstrate that falsity preserving principle and truth preserving principle are still valid.Finally,it presents the algorithms and example of upper quotient and lower quotient.The work extends the quotient space theory from structure,and provides theoretical basis for the combination of the quotient space theory and the algebra theory.

The rough representation and measurement of quotient structure in algebraic quotient space model

Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an equivalence relation. In this paper,definitions were given and formulas of the lower quotient congruence and upper quotient congruence were calculated to roughly represent the quotient structure. Then the accuracy and roughness were defined to measure the quotient structure in quantification. Finally,a numerical example was given to demonstrate that the rough representation and measuring methods are efficient and applicable. The work has greatly enriched the algebraic quotient space model and granular computing theory.

Dualities in Covering Rough Operations

Rough set theory is a technique of granular computing. In this paper, we study a type of generalized rough sets based on covering. There are several literatures[1,40-43] exploring covering-based rough sets. Our focus of this paper is on the dualities in rough operations.

Generalized multi-layered granulations and approximations based on neighborhood systems under incomplete information systems

A generalized multi-layered granulation structure used by neighborhood systems is proposed. With granulated views, the concepts of approximations under incomplete information systems are studied, which are represented by covering of the universe. With respect to different levels of granulations, a pair of lower and upper approximations is defined and an approximation structure is investigated, which lead to a more general approximation structure. The generalized multi-layered granulation structure provides a basis of the proposed framework of granular computing. Using this framework, the interesting and useful results about information granulation and approximation reasoning can be obtained. This paper presents some useful explorations about the incomplete information systems from information views.

A color image tracking method based on target characteristic hue decision

Conventional correlation matching algorithms waste great time in invalid area search. This paper proposes a color tracking method based on correlation search area optimization on target characteristic hue decision. By quantifying and reducing dimensions of HSV（ hue saturation value） color space, a one-dimensional hue space is constructed. In the space, the target characteristic hue granule set is constructed, which contains attributes such as value, area and average distance between pixels and aiming center. By using granular computing method, the similarity between target and search blocks is obtained and the invalid search areas can be removed. The color tracking experiment has proved that the algorithm can improve real time performance for conventional matching algorithms without precision lost.

Constraint-Based Fuzzy Models for an Environment with Heterogeneous Information-Granules

A novel framework for fuzzy modeling and model-based control design is described. Based on the theory of fuzzy constraint processing, the fuzzy model can be viewed as a generalized Takagi-Sugeno （TS） fuzzy model with fuzzy functional consequences. It uses multivariate antecedent membership functions obtained by granular-prototype fuzzy clustering methods and consequent fuzzy equations obtained by fuzzy regression techniques. Constrained optimization is used to estimate the consequent parameters, where the constraints are based on control-relevant a priori knowledge about the modeled process. The fuzzy-constraint-based approach provides the following features. 1） The knowledge base of a constraint-based fuzzy model can incorporate information with various types of fuzzy predicates. Consequently, it is easy to provide a fusion of different types of knowledge. The knowledge can be from data-driven approaches and/or from controlrelevant physical models. 2） A corresponding inference mechanism for the proposed model can deal with heterogeneous information granules. 3） Both numerical and linguistic inputs can be accepted for predicting new outputs. The proposed techniques are demonstrated by means of two examples： a nonlinear function-fitting problem and the well-known Box-Jenkins gas furnace process. The first example shows that the proposed model uses fewer fuzzy predicates achieving similar results with the traditional rule-based approach, while the second shows the performance can be significantly improved when the control-relevant constraints are considered.

Developing a GIS-based rough fuzzy set granulation model to handle spatial uncertainty for hydrocarbon structure classification,case study:Fars domain,Iran

It is well agreed that geologic risk occurs during hydrocarbon exploration because diverse uncertainties accompany the entire hydrocarbon system parameters such as the source rock,reservoir rock,trap and seal rock.In order to overcome such attributes with uncertainties,a number of soft computing methods are used.Information granules could be provided by the Rough Fuzzy Set Granulation(RFSG)with a thorough quality evaluation.This is capable of attribute reduction that has been claimed to be essential in investigating the hydrocarbon systems.This paper is an endeavor to recommend a Geospatial Information System(GIS)-based model with the aim of categorizing the hydrocarbon structures map consistent with the uncertainty range concepts of geologic risk in the rough fuzzy sets and granular computing.The model used the RFSG for the attribute reduction by a Decision Logic language(DLlanguage).The RFSG was employed in order to classify hydrocarbon structures according to geological risk and extract the fuzzy rules with a predefined range of uncertainty.In order to assess the precisions of the fuzzy decisions on the hydrocarbon structure classification,the fuzzy entropy and fuzzy cross-entropy are applied.The proposed RFSG model applied for 62 structures as the training data,average fuzzy entropy has been calculated as 0.85,whereas the average fuzzy cross-entropy has been calculated 0.18.As it can be discerned,just seven structures had cross-entropies greater than 0.1,while three structures were larger than 0.3.It is implied that the precision of the proposed model is about 89%.The results yielded two reductions for the condition attributes and 11 fuzzy rules being filtered by the granular computing values.

A variable precision rough set approach to knowledge discovery in land cover classification

This paper presents a granular computing approach to spatial classification and prediction of land cover classes using rough set variable precision methods.In particular,it presents an approach to characterizing large spatially clustered data sets to discover knowledge in multi-source supervised classification.The evidential structure of spatial classification is founded on the notions of equivalence relations of rough set theory.It allows expressing spatial concepts in terms of approximation space wherein a decision class can be approximated through the partition of boundary regions.The paper also identifies how approximate reasoning can be introduced by using variable precision rough sets in the context of land cover characterization.The rough set theory is applied to demonstrate an empirical application and the predictive performance is compared with popular baseline machine learning algorithms.A comparison shows that the predictive performance of the rough set rule induction is slightly higher than the decision tree and significantly outperforms the baseline models such as neural network,naïve Bayesian and support vector machine methods.