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The art of granular computing:
 Proceeding of the International Conference on Rough Sets and Emerging Intelligent Systems Paradigms,
, 2007
"... Abstract: This paper has two purposes. One is to present a critical examination of the rise of granular computing and the other is to suggest a triarchic theory of granular computing. By examining the reasons, justifications, and motivations for the rise of granular computing, we may be able to ful ..."
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Abstract: This paper has two purposes. One is to present a critical examination of the rise of granular computing and the other is to suggest a triarchic theory of granular computing. By examining the reasons, justifications, and motivations for the rise of granular computing, we may be able to fully appreciate its scope, goal and potential values. The results enable us to formulate a triarchic theory in the light of research results from many disciplines. The three components of the theory are labeled as the philosophy, the methodology, and the computation. The integration of the three offers a unified view of granular computing as a way of structured thinking, a method of structured problem solving, and a paradigm of structured information processing, focusing on hierarchical granular structures. The triarchic theory is an important effort in synthesizing the various theories and models of granular computing. Key words: Triarchic theory of granular computing; systems theory; structured thinking, problem solving and information processing. CLC number: Document code: A Introduction Although granular computing, as a separate field of study, started a decade ago [1], its basic philosophy, ideas, principles, methodologies, theories and tools has, in fact, long been used either explicitly or implicitly across many branches of natural and social sciences The answers, at least partial answers, to these questions may be obtained by drawing and synthesizing results from wellestablished disciplines, including philosophy, psychology, neuroscience, cognitive science, education, artificial intelligence, computer programming, and many more. Previously, I argued that granular computing represents an idea converged from many branches of natural and social sciences HumanInspired Computing Research on understanding the human brain and natural intelligence is closely related to the field of artificial intelligence (AI) and information technology (IT). The results have led to a computational view for explaining how the mind works
Attribute Reduction in DecisionTheoretic Rough Set Models
 INFORMATION SCIENCES, 178(17), 33563373, ELSEVIER B.V.
, 2008
"... Rough set theory can be applied to rule induction. There are two different types of classification rules, positive and boundary rules, leading to different decisions and consequences. They can be distinguished not only from the syntax measures such as confidence, coverage and generality, but also th ..."
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Cited by 29 (2 self)
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Rough set theory can be applied to rule induction. There are two different types of classification rules, positive and boundary rules, leading to different decisions and consequences. They can be distinguished not only from the syntax measures such as confidence, coverage and generality, but also the semantic measures such as decisionmonotocity, cost and risk. The classification rules can be evaluated locally for each individual rule, or globally for a set of rules. Both the two types of classification rules can be generated from, and interpreted by, a decisiontheoretic model, which is a probabilistic extension of the Pawlak rough set model. As an important concept of rough set theory, an attribute reduct is a subset of attributes that are jointly sufficient and individually necessary for preserving a particular property of the given information table. This paper addresses attribute reduction in decisiontheoretic rough set models regarding different classification properties, such as: decisionmonotocity, confidence, coverage, generality and cost. It is important to note that many of these properties can be truthfully reflected by a single measure γ in the Pawlak rough set model. On the other hand, they need to be considered separately in probabilistic models. A straightforward extension of the γ measure is unable to evaluate these properties. This study provides a new insight into the problem of attribute reduction.
On generalizing rough set theory
 Proceedings of 9th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, RSFDGrC’03
, 2003
"... Abstract. This paper summarizes various formulations of the standard rough set theory. It demonstrates how those formulations can be adopted to develop different generalized rough set theories. The relationships between rough set theory and other theories are discussed. 1 Formulations of Standard Ro ..."
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Cited by 21 (5 self)
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Abstract. This paper summarizes various formulations of the standard rough set theory. It demonstrates how those formulations can be adopted to develop different generalized rough set theories. The relationships between rough set theory and other theories are discussed. 1 Formulations of Standard Rough Sets The theory of rough sets can be developed in at least two different manners, the constructive and algebraic methods [16–20, 25, 29]. The constructive methods define rough set approximation operators using equivalence relations or their induced partitions and subsystems; the algebraic methods treat approximation operators as abstract operators. 1.1 Constructive methods Suppose U is a finite and nonempty set called the universe. Let E ⊆ U × U be an equivalence relation on U. The pair apr = (U, E) is called an approximation space [6, 7]. A few definitions of rough set approximations can be given based on different representations of an equivalence relation.
Granular computing for data mining
 Proceedings of SPIE Conference on Data Mining, Intrusion Detection, Information Assurance, and Data Networks Security
, 2006
"... Granular computing, as an emerging research field, provides a conceptual framework for studying many issues in data mining. This paper examines some of those issues, including data and knowledge representation and processing. It is demonstrated that one of the fundamental tasks of data mining is sea ..."
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Cited by 7 (2 self)
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Granular computing, as an emerging research field, provides a conceptual framework for studying many issues in data mining. This paper examines some of those issues, including data and knowledge representation and processing. It is demonstrated that one of the fundamental tasks of data mining is searching for the right level of granularity in data and knowledge representation. 1.
Rough set model selection for practical decision making
 IN: PROCEEDING OF FUZZY SYSTEMS AND KNOWLEDGE DISCOVERY (FSKD’07). III
, 2007
"... One of the challenges a decision maker faces is choosing a suitable rough set model to use for data analysis. The traditional algebraic rough set model classifies objects into three regions, namely, the positive, negative, and boundary regions. Two different probabilistic models, variableprecision a ..."
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Cited by 7 (4 self)
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One of the challenges a decision maker faces is choosing a suitable rough set model to use for data analysis. The traditional algebraic rough set model classifies objects into three regions, namely, the positive, negative, and boundary regions. Two different probabilistic models, variableprecision and decisiontheoretic, modify these regions via l,u userdefined thresholds and α, β values from loss functions respectively. A decision maker whom uses these models must know what type of decisions can be made within these regions. This will allow him or her to conclude which model is best for their decision needs. We present an outline that can be used to select a model and better analyze the consequences and outcomes of those decisions.
A unified framework of granular computing
 In: Handbook of Granular Computing
, 2008
"... In this chapter, we propose a unified framework for a holistic understanding of granular computing. It is developed based on three perspectives, namely, the philosophical, the methodological, and the computational perspectives. The three perspectives lead to structured thinking, structured problem s ..."
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Cited by 6 (2 self)
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In this chapter, we propose a unified framework for a holistic understanding of granular computing. It is developed based on three perspectives, namely, the philosophical, the methodological, and the computational perspectives. The three perspectives lead to structured thinking, structured problem solving, and structured information processing. We argue that the subject of the study of granular computing is a web of interacting granules representing a problem to be solved. From the web of granules, one can derive descriptions with multiple hierarchies (i.e., multiview) and multilevel granularity in each hierarchy.
Semantics of Fuzzy Sets in Rough Set Theory
 LNCS Transactions on Rough Sets
, 2004
"... Abstract. The objective of this chapter is to provide a semantic framework for fuzzy sets in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. The relationships between fuzzy membership funct ..."
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Abstract. The objective of this chapter is to provide a semantic framework for fuzzy sets in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. The relationships between fuzzy membership functions and rough membership functions, between core and support of fuzzy set theory and lower and upper approximation of rough set theory, are investigated. It is demonstrated that both theories share the same qualitative properties. Interpretations of fuzzy sets in rough set theory lead to constraints on membership values. Two types of constraints on membership values are studies, namely, constraints on membership values of related elements and constraints on membership values of related sets. The classical rough set model and generalized rough set models are discussed. 1
Granular computing: Granular classifiers and missing values
 In: Proceedings IEEE ICCI07, Lake Tahoe NV
, 2007
"... Abstract — Granular Computing is a paradigm destined to study how to compute with granules of knowledge that are collective objects formed from individual objects by means of a similarity measure. The idea of granulation was put forth by Lotfi Zadeh: granulation is inculcated in fuzzy set theory by ..."
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Abstract — Granular Computing is a paradigm destined to study how to compute with granules of knowledge that are collective objects formed from individual objects by means of a similarity measure. The idea of granulation was put forth by Lotfi Zadeh: granulation is inculcated in fuzzy set theory by the very definition of a fuzzy set and inverse values of fuzzy membership functions are elementary forms of granules. Similarly, rough sets admit granules defined naturally as classes of indiscernibility relations; the search for more flexible granules has led to granules based on blocks (Grzymala–Busse), templates (H.S.Nguyen), rough inclusions (Polkowski, Skowron), and tolerance or similarity relations, and more generally, binary relations (T.Y. Lin, Y. Y. Yao). Rough inclusions establish a form of similarity relations
DecisionTheoretic Rough Set Models (DTRSM)
, 2008
"... The standard rough sets model is a qualitative model that defines three regions for approximating a subset of a universe of objects based on an equivalence relation on the universe. The positive region (i.e., the lower approximation) is the union of equivalence classes that are subsets of the set to ..."
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The standard rough sets model is a qualitative model that defines three regions for approximating a subset of a universe of objects based on an equivalence relation on the universe. The positive region (i.e., the lower approximation) is the union of equivalence classes that are subsets of the set to be approximated. The boundary region (i.e., the difference of upper approximation and lower approximation) is the union of equivalence classes that have nonempty intersections with the set and at the same time are not subsets of the set. The negative region (i.e., the complement of the upper approximations) is the union of equivalence classes that have an empty intersection with the set. The theory may be formulated and interpreted in terms of threevalued logic, in which each value corresponds to one of the three regions. More importantly, the threevalued logic is nontruthfunctional, that is, one may not be able to obtain the value of compound formula based on its component subformulas. A lack of consideration of the degree of overlap between an equivalence class and the set motivates many researchers to study quantitative rough set models. Probabilistic approaches to rough sets are one of the most important and successful schools of quantitative rough sets. The DecisionTheoretic Rough Set Model (DTRSM) was proposed in early 1990’s based on the wellestablished
Towards Granular Computing: Classifiers Induced From Granular Structures
"... Abstract. 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 gran ..."
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Abstract. 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