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Rough sets: some extensions,”
 Information Sciences,
, 2007
"... Abstract In this article, we present some extensions of the rough set approach and we outline a challenge for the rough set based research. ..."
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Cited by 87 (6 self)
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Abstract In this article, we present some extensions of the rough set approach and we outline a challenge for the rough set based research.
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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Cited by 74 (20 self)
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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
A Partition Model of Granular Computing
 LNCS Transactions on Rough Sets
, 2004
"... There are two objectives of this chapter. One objective is to examine the basic principles and issues of granular computing. We focus on the tasks of granulation and computing with granules. From semantic and algorithmic perspectives, we study the construction, interpretation, and representation ..."
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Cited by 45 (14 self)
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There are two objectives of this chapter. One objective is to examine the basic principles and issues of granular computing. We focus on the tasks of granulation and computing with granules. From semantic and algorithmic perspectives, we study the construction, interpretation, and representation of granules, as well as principles and operations of computing and reasoning with granules. The other objective is to study a partition model of granular computing in a settheoretic setting. The model is based on the assumption that a finite set of universe is granulated through a family of pairwise disjoint subsets. A hierarchy of granulations is modeled by the notion of the partition lattice.
Probabilistic approaches to rough sets
 Expert Systems
, 2003
"... This paper reviews probabilistic approaches to rough sets in granulation, approximation, and rule induction. The Shannon entropy function is used to quantitatively characterize partitions of a universe. Both algebraic and probabilistic rough set approximations are studied. The probabilistic approxim ..."
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Cited by 22 (10 self)
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This paper reviews probabilistic approaches to rough sets in granulation, approximation, and rule induction. The Shannon entropy function is used to quantitatively characterize partitions of a universe. Both algebraic and probabilistic rough set approximations are studied. The probabilistic approximations are defined in a decisiontheoretic framework. The problem of rule induction, a major application of rough set theory, is studied in probabilistic and informationtheoretic terms. Two types of rules are analyzed, the local, low order rules, and the global, high order rules. 1
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.
Rough Approximation Quality Revisited
, 2001
"... In rough set theory, the approximation quality # is the traditional measure to evaluate the classification success of attributes in terms of a numerical evaluation of the dependency properties generated by these attributes. In this paper we reinterpret the classical # in terms of a classic measure ..."
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Cited by 16 (5 self)
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In rough set theory, the approximation quality # is the traditional measure to evaluate the classification success of attributes in terms of a numerical evaluation of the dependency properties generated by these attributes. In this paper we reinterpret the classical # in terms of a classic measure based on sets, the MarczewskiSteinhaus metric, and also in terms of "proportional reduction of errors" (PRE) measures. We also exhibit infinitely many possibilities to define # like statistics which are meaningful in situations different from the classical one, and provide tools to ascertain the statistical significance of the proposed measures, which are valid for any kind of sample. 2001 Published by Elsevier Science B.V.
Uncertainty measures for fuzzy relations and their applications
, 2006
"... Relations and relation matrices are important concepts in set theory and intelligent computation. Some general uncertainty measures for fuzzy relations are proposed by generalizing Shannon’s information entropy. Then, the proposed measures are used to calculate the diversity quantity of multiple cla ..."
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Cited by 14 (0 self)
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Relations and relation matrices are important concepts in set theory and intelligent computation. Some general uncertainty measures for fuzzy relations are proposed by generalizing Shannon’s information entropy. Then, the proposed measures are used to calculate the diversity quantity of multiple classifier systems and the granularity of granulated problem spaces, respectively. As a diversity measure, it is shown that the fusion system whose classifiers are of little similarity produces a great uncertainty quantity, which means that much complementary information is achieved with a diverse multiple classifier system. In granular computing, a ‘‘coarse–fine’ ’ order is introduced for a family of problem spaces with the proposed granularity measures. The problem space that is finely granulated will get a great uncertainty quantity compared with the coarse problem space. Based on the observation, we employ the proposed measure to evaluate the significance of numerical attributes for classification. Each numerical attribute generates a fuzzy similarity relation over the sample space. We compute the condition entropy of a numerical attribute or a set of numerical attribute relative to the decision, where the greater the condition entropy is, the less important the attribute subset is. A forward greedy search algorithm for numerical feature selection is constructed with the proposed measure. Experimental results show that the proposed method presents an efficient and effective solution for numerical feature analysis.
Information granulation and approximation in a decisiontheoretical model of rough sets
, 2003
"... Summary. Granulation of the universe and approximation of concepts in the granulated universe are two related fundamental issues in the theory of rough sets. Many proposals dealing with the two issues have been made and studied extensively. We present a critical review of results from existing studi ..."
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Cited by 13 (8 self)
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Summary. Granulation of the universe and approximation of concepts in the granulated universe are two related fundamental issues in the theory of rough sets. Many proposals dealing with the two issues have been made and studied extensively. We present a critical review of results from existing studies that are relevant to a decisiontheoretic modeling of rough sets. Two granulation structures are studied, one is a partition induced by an equivalence relation and the other is a covering induced by a reflexive relation. With respect to the two granulated views of the universe, element oriented and granule oriented definitions and interpretations of lower and upper approximation operators are examined. The structures of the families of fixed points of approximation operators are investigated. We start with the notions of rough membership functions and graded set inclusion defined by conditional probability. This enables us to examine different granulation structures and the induced approximations in a decisiontheoretic setting. By reviewing and combining results from existing studies, we attempt to establish a solid foundation for rough sets and to provide a systematic way for determining the required parameters in defining approximation operators. 1
Granular computing: past, present, and future
 Proceedings of RSKT’08, LNAI 5009
, 2008
"... Granular computing is gradually changing from a label to a new field of study. The driving forces, the major schools of thought, and the future research directions on granular computing are examined. A triarchic theory of granular computing is outlined. Granular computing is viewed as an interdiscip ..."
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Cited by 10 (5 self)
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Granular computing is gradually changing from a label to a new field of study. The driving forces, the major schools of thought, and the future research directions on granular computing are examined. A triarchic theory of granular computing is outlined. Granular computing is viewed as an interdisciplinary study of humaninspired computing, characterized by structured thinking, structured problem solving, and structured information processing.
Information Granulation for Web based Information Retrieval Support Systems
 Proceedings of SPIE
, 2003
"... In this paper, we discuss the potential applications of data mining techniques for the design of Web based information retrieval support systems (IRSS). In particular, we apply clustering methods for the granulation of di#erent entities involved in IRSS. Two types of granulations, singlelevel and m ..."
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Cited by 9 (3 self)
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In this paper, we discuss the potential applications of data mining techniques for the design of Web based information retrieval support systems (IRSS). In particular, we apply clustering methods for the granulation of di#erent entities involved in IRSS. Two types of granulations, singlelevel and multilevel granulations, are investigated. Issues of document space granulation, query space granulation, term space granulation, and retrieval results granulation are studied in detail. It is demonstrated that each di#erent granulation supports a di#erent user task.