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22
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.
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.
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 22 (7 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
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
ThreeWay Decision: An Interpretation of Rules in Rough Set Theory
"... Abstract. A new interpretation of rules in rough set theory is introduced. According to the positive, boundary, and negative regions of a set, one can make a threeway decision: accept, abstain and reject. The three regions enable us to derive three types of decision rules, namely, positive rules fo ..."
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Cited by 4 (4 self)
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Abstract. A new interpretation of rules in rough set theory is introduced. According to the positive, boundary, and negative regions of a set, one can make a threeway decision: accept, abstain and reject. The three regions enable us to derive three types of decision rules, namely, positive rules for acceptance, boundary rules for indecision or delayed decision, and negative rules for rejection. Within the decisiontheoretic rough set model, the associated costs of rules are analyzed. 1
Notes on Rough Set Approximations and Associated Measures
"... We review and compare two definitions of rough set approximations. One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe. The latter definition, although less studied, is semantically superior for interpreting rule induction and is closely related ..."
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Cited by 3 (0 self)
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We review and compare two definitions of rough set approximations. One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe. The latter definition, although less studied, is semantically superior for interpreting rule induction and is closely related to granularity switching in granular computing. Numerical measures about the accuracy and quality of approximations are examined. Several semantics difficulties are commented.
Learning Optimal Parameters in DecisionTheoretic Rough Sets
"... Abstract. A gametheoretic approach for learning optimal parameter values for probabilistic rough set regions is presented. The parameters can be used to define approximation regions in a probabilistic decision space. New values for loss functions are learned from a sequence of risk modifications de ..."
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Cited by 3 (1 self)
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Abstract. A gametheoretic approach for learning optimal parameter values for probabilistic rough set regions is presented. The parameters can be used to define approximation regions in a probabilistic decision space. New values for loss functions are learned from a sequence of risk modifications derived from gametheoretic analysis of the relationship between two classification measures. Using game theory to maximize these measures results in a learning method to reformulate the loss functions. The decisiontheoretic rough set model acquires initial values for these parameters through a combination of loss functions provided by the user. The new gametheoretic learning method modifies these loss functions according to an acceptable threshold. 1
A gametheoretic perspective on rough set analysis
 JOURNAL OF CHONGQING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS
, 2008
"... Determining the correct threshold values for the probabilistic rough set approaches has been a heated issue among the community. Existing techniques offer no way in guaranteeing that the calculated values optimize the classification ability of the decision rules derived from this configuration. This ..."
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Cited by 3 (2 self)
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Determining the correct threshold values for the probabilistic rough set approaches has been a heated issue among the community. Existing techniques offer no way in guaranteeing that the calculated values optimize the classification ability of the decision rules derived from this configuration. This article will formulate a game theoretic approach to calculating these thresholds to ensure correct approximation region size. Using 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. This will aid in determining a set of optimal region threshold values for decision making.
Stochastic Dominancebased Rough Set Model for Ordinal Classification
"... In order to discover interesting patterns and dependencies in data, an approach based on rough set theory can be used. In particular, Dominancebased Rough Set Approach (DRSA) has been introduced to deal with the problem of ordinal classification with monotonicity constraints (also referred to as mu ..."
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Cited by 2 (2 self)
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In order to discover interesting patterns and dependencies in data, an approach based on rough set theory can be used. In particular, Dominancebased Rough Set Approach (DRSA) has been introduced to deal with the problem of ordinal classification with monotonicity constraints (also referred to as multicriteria classification in decision analysis). However, in reallife problems, in the presence of noise, the notions of rough approximations were found to be excessively restrictive. In this paper, we introduce a probabilistic model for ordinal classification problems with monotonicity constraints. Then, we generalize the notion of lower approximations to the stochastic case. We estimate the probabilities with the maximum likelihood method which leads to the isotonic regression problem for a twoclass (binary) case. The approach is easily generalized to a multiclass case. Finally, we show the equivalence of the variable consistency rough sets to the specific empirical riskminimizing decision rule in the statistical decision theory. 1
Naive Bayesian rough sets
 Proceedings of RSKT 2010, LNAI 6401
, 2010
"... Abstract. A naive Bayesian classifier is a probabilistic classifier based on Bayesian decision theory with naive independence assumptions, which is often used for ranking or constructing a binary classifier. The theory of rough sets provides a ternary classification method by approximating a set int ..."
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Abstract. A naive Bayesian classifier is a probabilistic classifier based on Bayesian decision theory with naive independence assumptions, which is often used for ranking or constructing a binary classifier. The theory of rough sets provides a ternary classification method by approximating a set into positive, negative and boundary regions based on an equivalence relation on the universe. In this paper, we propose a naive Bayesian decisiontheoretic rough set model, or simply a naive Bayesian rough set (NBRS) model, to integrate these two classification techniques. The conditional probability is estimated based on the Bayes ’ theorem and the naive probabilistic independence assumption. A discriminant function is defined as a monotonically increasing function of the conditional probability, which leads to analytical and computational simplifications.