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Information granulation and rough set approximation
 International Journal of Intelligent Systems
, 2001
"... Information granulation and concept approximation are some of the fundamental issues of granular computing. Granulation of a universe involves grouping of similar elements into granules to form coarsegrained views of the universe. Approximation of concepts, represented by subsets of the universe, d ..."
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Cited by 43 (17 self)
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Information granulation and concept approximation are some of the fundamental issues of granular computing. Granulation of a universe involves grouping of similar elements into granules to form coarsegrained views of the universe. Approximation of concepts, represented by subsets of the universe, deals with the descriptions of concepts using granules. In the context of rough set theory, this paper examines the two related issues. The granulation structures used by standard rough set theory and the corresponding approximation structures are reviewed. Hierarchical granulation and approximation structures are studied, which results in stratified rough set approximations. A nested sequence of granulations induced by a set of nested equivalence relations leads to a nested sequence of rough set approximations. A multilevel granulation, characterized by a special class of equivalence relations, leads to a more general approximation structure. The notion of neighborhood systems is also explored. 1
A decision theoretic framework for approximating concepts
 International Journal of Manmachine Studies
, 1992
"... This paper explores the implications of approximating a concept based on the Bayesian decision procedure, which provides a plausible unification of the fuzzy set and rough set approaches for approximating a concept. We show that if a given concept is approximated by one set, the same result given by ..."
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Cited by 41 (22 self)
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This paper explores the implications of approximating a concept based on the Bayesian decision procedure, which provides a plausible unification of the fuzzy set and rough set approaches for approximating a concept. We show that if a given concept is approximated by one set, the same result given by the αcut in the fuzzy set theory is obtained. On the other hand, if a given concept is approximated by two sets, we can derive both the algebraic and probabilistic rough set approximations. Moreover, based on the well known principle of maximum (minimum) entropy, we give a useful interpretation of fuzzy intersection and union. Our results enhance the understanding and broaden the applications of both fuzzy and rough sets. 1.
Discovery of Data Patterns with Applications to Decomposition and Classification Problems
, 1998
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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 21 (9 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
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 21 (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.
Threeway decisions with probabilistic rough sets
 Information Sciences
, 2010
"... The rough set theory approximates a concept by three regions, namely, the positive, boundary and negative regions. Rules constructed from the three regions are associated with different actions and decisions, which immediately leads to the notion of threeway decision rules. A positive rule makes a ..."
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Cited by 18 (6 self)
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The rough set theory approximates a concept by three regions, namely, the positive, boundary and negative regions. Rules constructed from the three regions are associated with different actions and decisions, which immediately leads to the notion of threeway decision rules. A positive rule makes a decision of acceptance, a negative rule makes a decision of rejection, and a boundary rule makes a decision of abstaining. This paper provides an analysis of threeway decision rules in the classical rough set model and the decisiontheoretic rough set model. The results enrich the rough set theory by ideas from Bayesian decision theory and hypothesis testing in statistics. The connections established between the levels of tolerance for errors and costs of incorrect decisions make the rough set theory practical in applications. Key words: Decisiontheoretic rough sets; probabilistic rough sets; threeway decisions; hypothesis testing; Bayesian decision procedure; classification 1
Potential Applications of Granular Computing in Knowledge Discovery and Data Mining
, 1999
"... In this paper, we argue that granular computing may have many potential applications in knowledge discovery and data mining. Three related basic operations of granular computing are examined: granulation of the universe, characterization of granules, and relationships between granules. Their connect ..."
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Cited by 17 (8 self)
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In this paper, we argue that granular computing may have many potential applications in knowledge discovery and data mining. Three related basic operations of granular computing are examined: granulation of the universe, characterization of granules, and relationships between granules. Their connections to the tasks of knowledge discovery and data mining are analyzed.
GameTheoretic Risk Analysis in DecisionTheoretic Rough Sets
"... Abstract. Determining the correct threshold values for probabilistic rough set models has been a heated issue among the community. This article will formulate a gametheoretic approach to calculating these thresholds to ensure correct approximation region size. By finding equilibrium within payoff t ..."
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Cited by 7 (3 self)
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Abstract. Determining the correct threshold values for probabilistic rough set models has been a heated issue among the community. This article will formulate a gametheoretic approach to calculating these thresholds to ensure correct approximation region size. By finding equilibrium within payoff tables created from approximation measures and modified conditional risk strategies, we provide the user with tolerance levels for their loss functions. Using the tolerance values, new thresholds are calculated to provide correct classification regions. Better informed decisions can be made when utilizing these tolerance values. 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.