Browsing by Author "Fan, Tuan-Fang"

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A LOGICAL FORMULATION OF ROUGH SET DEFINABILITY
(2011-02-01)
Fan, Tuan-Fang
;
Liau, Churn-Jung
;
Liu, Duen-Ren
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
In data mining problems, data is usually provided in the form of data tables. To represent knowledge discovered from data tables, a decision logic (DL) is proposed in rough set theory. DL, is an instance of propositional logic, but we can use other logical formalisms to describe data tables. In this paper, we propose two descriptions of data tables based on first-order data logic (FOUL) and attribute value-sorted logic (AVSL) respectively. In the context of FODL, we show that explicit, definability and implicit definability in classical logic implies the notion of definability in rough set theory. We also show that AVSL is particularly useful for the representation of properties of many-valued data tables.
A relational perspective of attribute reduction in rough set-based data analysis
(2011-08-16)
Fan, Tuan-Fang
;
Liau, Churn-Jung
;
Liu, Duen-Ren
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Attribute reduction is very important in rough set-based data analysis (RSDA) because it can be used to simplify the induced decision rules without reducing the classification accuracy. The notion of reduct plays a key role in rough set-based attribute reduction. In rough set theory, a reduct is generally defined as a minimal subset of attributes that can classify the same domain of objects as unambiguously as the original set of attributes. Nevertheless, from a relational perspective, RSDA relies on a kind of dependency principle. That is, the relationship between the class labels of a pair of objects depends on component-wise comparison of their condition attributes. The larger the number of condition attributes compared, the greater the probability that the dependency will hold. Thus, elimination of condition attributes may cause more object pairs to violate the dependency principle. Based on this observation, a reduct can be defined alternatively as a minimal subset of attributes that does not increase the number of objects violating the dependency principle. While the alternative definition coincides with the original one in ordinary RSDA, it is more easily generalized to cases of fuzzy RSDA and relational data analysis. (C) 2010 Elsevier B.V. All rights reserved.
A Uniform Framework for Rough Approximations Based on Generalized Quantifiers
(2015-01-01)
Fan, Tuan-Fang
;
Liau, Churn-Jung
;
Liu, Duen-Ren
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
The rough set theory provides an effective tool for decision analysis in the way of extracting decision rules from information systems. The rule induction process is based on the definitions of lower and upper approximations of the decision class. The condition attributes of the information system constitute an indiscernibility relation on the universe of objects. An object is in the lower approximation of the decision class if all objects indiscernible with it are in the decision class and it is in the upper approximation of the decision class if some objects indiscernible with it are in the decision class. Various generalizations of rough set theory have been proposed to enhance the capability of the theory. For example, variable precision rough set theory is used to improve the robustness of rough set analysis and fuzzy rough set approach is proposed to deal with vague information. In this paper, we present a uniform framework for different variants of rough set theory by using generalized quantifiers. In the framework, the lower and upper approximations of classical rough set theory are defined with universal and existential quantifiers respectively, whereas variable precision rough approximations correspond to probability quantifiers. Moreover, fuzzy rough set approximations can be defined by using different fuzzy quantifiers. We show that the framework can enhance the expressive power of the decision rules induced by rough set-based decision analysis.
Arrow decision logic for relational information systems
(2006)
Fan, Tuan-Fang
;
Liu, Duen-Ren
;
Tzeng, Gwo-Hshiung
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
In this paper, we propose an arrow decision logic (ADL) for relational information systems (RIS). The logic combines the main features of decision logic (DL) and arrow logic (AL). DL represents and reasons about knowledge extracted from decision tables based on rough set theory, whereas AL is the basic modal logic of arrows. The semantic models of DL are functional information systems (FIS). ADL formulas, on the other hand, are interpreted in RIS. RIS, which not only specifies the properties of objects, but also the relationships between objects. We present a complete axiomatization of ADL and discuss its application to knowledge representation in multicriteria decision analysis.
Constraint-Based Attribute Reduction in Rough Set Analysis
(2010-01-01)
Fan, Tuan-Fang
;
Liau, Churn-Jung
;
Liu, Duen-Ren
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Attribute reduction is very important in rough set-based data analysis (RSDA) because it can be used to simplify the induced decision rules without reducing the classification accuracy. The notion of reduct plays a key role in rough set-based attribute reduction. In rough set theory, a reduct is generally defined as a minimal subset of attributes that can classify the same domain of objects as unambiguously as the original set of attributes. Nevertheless, from a relational perspective, RSDA relies on a kind of dependency constraint. That is, the relationship between the class labels of a pair of objects depends on the componentwise comparison of their condition attributes. The larger the number of condition attributes compared, the greater the probability that the constraint will hold. Thus, elimination of condition attributes may cause more object pairs to violate the constraint. Based on this observation, a reduct can be defined alternatively as a minimal subset of attributes that does not increase the number of objects violating the constraint. While the alternative definition coincides with the original one in ordinary RSDA, it is more easily generalized to cases of fuzzy RSDA and relational data analysis.
Definability in Logic and Rough Set Theory
(2008-01-01)
Fan, Tuan-Fang
;
Liau, Churn-Jung
;
Liu, Duen-Ren
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Rough set theory is an effective tool for data mining. According to the theory, a concept is definable if it can be written as a Boolean combination of equivalence classes induced from classification attributes. On the other hand, definability in logic has been explicated by Beth's theorem. In this paper, we propose two data representation formalisms, called first-order data logic (FODL) and attribute value-sorted logic (AVSL), respectively. Based on these logics, we explore the relationship between logical definability and rough set definability.
Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables
(2011-12-01)
Fan, Tuan-Fang
;
Liau, Churn-Jung
;
Liu, Duen-Ren
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
In this paper, we propose a dominance-based fuzzy rough set approach for the decision analysis of a preference-ordered uncertain or possibilistic data table, which is comprised of a finite set of objects described by a finite set of criteria. The domains of the criteria may have ordinal properties that express preference scales. In the proposed approach, we first compute the degree of dominance between any two objects based on their imprecise evaluations with respect to each criterion. This results in a valued dominance relation on the universe. Then, we define the degree of adherence to the dominance principle by every pair of objects and the degree of consistency of each object. The consistency degrees of all objects are aggregated to derive the quality of the classification, which we use to define the reducts of a data table. In addition, the upward and downward unions of decision classes are fuzzy subsets of the universe. Thus, the lower and upper approximations of the decision classes based on the valued dominance relation are fuzzy rough sets. By using the lower approximations of the decision classes, we can derive two types of decision rules that can be applied to new decision cases. (C) 2011 Elsevier Inc. All rights reserved.
Dominance-based Rough Set Analysis of Uncertain Data Tables
(2009-01-01)
Fan, Tuan-Fang
;
Liau, Churn-Jung
;
Liu, Duen-Ren
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
In this paper, we propose a dominance-based rough set approach for the decision analysis of a preference-ordered uncertain data table, which is comprised of a finite set of objects described by a finite set of criteria. The domains of the criteria may have ordinal properties that express preference scales. In the proposed approach, we first compute the degree of dominance between any two objects based on their imprecise evaluations with respect to each criterion. This results in a fuzzy dominance relation on the universe. Then, we define the degree of adherence to the dominance principle by every pair of objects and the degree of consistency of each object. The consistency degrees of all objects are aggregated to derive the quality of the classification, with which we can define the reducts of an uncertain data table. In addition, the upward and downward unions of decision classes are fuzzy subsets of the universe. The lower and upper approximations of the decision classes based on the fuzzy dominance relation are thus fuzzy rough sets. By using the lower approximations of the decision classes, we can derive two types of decision rules that can be applied to new decision cases.
Dominance-Based Rough Set Approach for Possibilistic Information Systems
(2011)
Fan, Tuan-Fang
;
Liau, Churn-Jung
;
Liu, Duen-Ren
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
In this paper, we propose a dominance-based fuzzy rough set approach for the decision analysis of a preference-ordered possibilistic information systems, which is comprised of a finite set of objects described by a finite set of criteria. The domains of the criteria may have ordinal properties that express preference scales. In the proposed approach, we first compute the degree of dominance between any two objects based on their possibilistic evaluations with respect to each criterion. This results in a fuzzy dominance relation on the universe. Then, we define the degree of adherence to the dominance principle by every pair of objects and the degree of consistency of each object. The consistency degrees of all objects are aggregated to derive the quality of the classification, which we use to define the reducts of an information system. In addition, the upward and downward unions of decision classes are fuzzy subsets of the universe. The lower and upper approximations of the decision classes based on the fuzzy dominance relation are thus fuzzy rough sets. By using the lower approximations of the decision classes, we can derive two types of decision rules that can be applied to new decision cases.
Positional analysis in fuzzy social networks
(2007)
Fan, Tuan-Fang
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Liaut, Churn-Jung
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Lin, Tsau-Young
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Social network analysis is a methodology used extensively in social and behavioral sciences, as well as in political science, economics, organization theory, and industrial engineering. Positional analysis of a social network aims to find similarities between. actors in the network. One of the the most studied notions in the positional analysis of social networks is regular equivalence. According to Borgatti and Everett, two actors are regularly, equivalent if they are equally, related to equivalent others. In recent years, fuzzy social networks have also received considerable attention because the), can. represent both the qualitative relationship and the degrees of interaction between actors. In this paper, we generalize the notion of regular equivalence to fuzzy social networks based on. two alternative definitions of regular equivalence. While these two definitions are equivalent for social networks, they induce different generalizations for fuzzy social networks. The first generalization, called regular similarity, is based on. the characterization of regular equivalence as an equivalence relation that commutes with the underlying social relations. The regular similarity is then. a fuzzy binary, relation that specifies the degree of similarity between. actors in the social network. The second generalization, called generalized regular equivalence, is based on the definition of role assignment or coloring. A role assignment (resp. coloring) is a mapping, from the set of actors to a set of roles (resp. colors). The mapping is regular if actors assigned to the same role have the same roles in their neighborhoods. Consequently, generalized regular equivalence is an equivalence relation. that can determine the role partition of the actors in a fuzzy social network.
Rough set-based logics for multicriteria decision analysis
(2007-10-01)
Fan, Tuan-Fang
;
Liu, Duen-Ren
;
Tzeng, Gwo-Hshiung
;
科技管理研究所
;
資訊管理與財務金融系註：原資管所+財金所
In this paper, we propose some decision logic languages for rule representation in rough set-based multicriteria analysis. The semantic models of these logics are data tables, each of which is comprised of a finite set of objects described by a finite set of criteria/attributes. The domains of the criteria may have ordinal properties expressing preference scales, while the domains of the attributes may not. The validity, support, and confidence of a rule are defined via its satisfaction in the data table. (c) 2006 Elsevier B.V. All rights reserved.
Variable consistency and variable precision models for dominance-based fuzzy rough set analysis of possibilistic information systems
(2013-08-01)
Fan, Tuan-Fang
;
Liau, Churn-Jung
;
Liu, Duen-Ren
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
The dominance-based fuzzy rough set approach (DFRSA) is a theoretical framework that can deal with multi-criteria decision analysis of possibilistic information systems. While a set of comprehensive decision rules can be induced from a possibilistic information system by using DFRSA, generation of several intuitively justified rules is sometimes blocked by objects that only partially satisfy the antecedents of the rules. In this paper, we use the variable consistency models and variable precision models of DFRSA to cope with the problem. The models admit rules that are not satisfied by all objects. It is only required that the proportion of objects satisfying the rules must be above a threshold called a consistency level or a precision level. In the presented models, the proportion of objects is represented as a relative cardinality of a fuzzy set with respect to another fuzzy set. We investigate three types of models based on different definitions of fuzzy cardinalities including Sigma-counts, possibilistic cardinalities, and probabilistic cardinalities; and the consistency levels or precision levels corresponding to the three types of models are, respectively, scalars, fuzzy numbers, and random variables.
Variable Precision Fuzzy Rough Set Based on Relative Cardinality
(2012)
Fan, Tuan-Fang
;
Liau, Churn-Jung
;
Liu, Duen-Ren
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
The fuzzy rough set approach (FRSA) is a theoretical framework that can deal with data analysis of possibilistic information systems. While a set of comprehensive rules can be induced from a possibilistic information system by using FRSA, generation of several intuitively justified rules is sometimes blocked by objects that only partially satisfy the antecedents of the rules. In this paper, we use the variable precision models of FRSA to cope with the problem. The models admit rules that are not satisfied by all objects. It is only required that the proportion of objects satisfying the rules must be above a threshold called a a precision level. In the presented models, the proportion of objects is represented as a relative cardinality of a fuzzy set with respect to another fuzzy set. We investigate three types of models based on different definitions of fuzzy cardinalities including Sigma-counts, possibilistic cardinalities, and probabilistic cardinalities; and the precision levels corresponding to the three types of models are respectively scalars, fuzzy numbers, and random variables.