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1

Using One Axiom to Characterize Fuzzy Rough Approximation Operators Determined by a Fuzzy Implication Operator

Wu W.-Z., Li T-J., Gu S.-M.

Fundamenta Informaticae

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2015

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Vol. 142, nr 1-4

87--104

EN

Axiomatic characterizations of approximation operators are important in the study of rough set theory. In this paper, axiomatic characterizations of relation-based fuzzy rough approximation operators determined by a fuzzy implication operator I are investigated. We first review the constructive definitions and properties of lower and upper I-fuzzy rough approximation operators. We then propose an operator-oriented characterization of I-fuzzy rough sets. We show that the lower and upper I-fuzzy rough approximation operators generated by an arbitrary fuzzy relation can be described by single axioms. We further examine that I-fuzzy rough approximation operators corresponding to some special types of fuzzy relations, such as serial, reflexive, and T -transitive ones, can also be characterized by single axioms.

2

Applications of Fuzzy Rough Set Theory in Machine Learning : a Survey

Vluymans S., D’eer L., Saeys Y., Cornelis C.

Fundamenta Informaticae

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2015

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Vol. 142, nr 1-4

53--86

EN

Data used in machine learning applications is prone to contain both vague and incomplete information. Many authors have proposed to use fuzzy rough set theory in the development of new techniques tackling these characteristics. Fuzzy sets deal with vague data, while rough sets allow to model incomplete information. As such, the hybrid setting of the two paradigms is an ideal candidate tool to confront the separate challenges. In this paper, we present a thorough review on the use of fuzzy rough sets in machine learning applications. We recall their integration in preprocessing methods and consider learning algorithms in the supervised, unsupervised and semi-supervised domains and outline future challenges. Throughout the paper, we highlight the interaction between theoretical advances on fuzzy rough sets and practical machine learning tools that take advantage of them.

3

Fuzzy Rough Decision Trees

An S., Shi H., Hu Q., Dang J.

Fundamenta Informaticae

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2014

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Vol. 132, nr 3

381--399

EN

How to evaluate features and select nodes is one of the key issues in constructing decision trees. In this work fuzzy rough set theory is employed to design an index for evaluating the quality of fuzzy features or numerical attributes. A fuzzy rough decision tree algorithm, which can be used to address classification problems described with symbolic, real-valued or fuzzy features, is developed. As node selection, split generation and stopping criterion are three main factors in constructing a decision tree, we design different techniques to determine splits with different kinds of features. The proposed algorithm can directly generate a classification tree without discretization or fuzzification of continuous attributes. Some numerical experiments are conducted and the comparative results show that the proposed algorithm is effective compared with some popular algorithms.

4

Decision-theoretic Rough Sets in Incomplete Information System

Yang X., Lu Z., Li T-J.

Fundamenta Informaticae

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2013

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Vol. 126, nr 4

353--375

EN

Decision-theoretic rough sets in two kinds of incomplete information systems are discussed in this paper. One is for the classical decision attribute and the other for the fuzzy decision attribute. In complete information system, the universe is partitioned with the equivalence relation. Given a concept, we get a pair of approximations of the concept using rough set theory, and the universe can be partitioned into three regions for making a decision. An incomplete information table can be expressed as a family of complete information tables. The universe is partitioned by the equivalence relation for each complete information table. The probability of each object belonging to the concept can be calculated in a completion from incomplete information system, and then the total probability of the object belonging to the concept can be obtained. Decision rules are derived using total probability instead of conditional probability in decision-theoretic rough sets. Finally, the universe is divided into three regions according to the total probability. A similar approach to fuzzy incomplete information system is examined and the universe is also divided into three regions.

5

Soft Minimum-Enclosing-Ball Based Robust Fuzzy Rough Sets

An S., Hu Q., Yu D., Liu J.

Fundamenta Informaticae

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2012

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Vol. 115, nr 2/3

189-202

EN

The theory of fuzzy rough sets is claimed to be a powerful mathematical tool for dealing with uncertainty in data analysis. Unluckily, the classical model of fuzzy rough sets is sensitive to noisy information. This disadvantage limits the applicability of the model in practice. In this work, we present a robust fuzzy rough set model based on soft minimum enclosing ball, and introduce a new fuzzy dependency function with this model. Some properties of the new model are discussed. Finally, we conduct some experiments to test the effectiveness of the proposed model, and experimental results show that the soft minimum enclosing ball-based fuzzy rough set model is robust to noise.

6

The Construction of Fuzzy Concept Lattices Based on (θ,σ)-Fuzzy Rough Approximation Operators

Yao Y., Li Z., Mi J., Xie B.

Fundamenta Informaticae

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2011

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Vol. 111, nr 1

33-45

EN

Formal concept analysis and rough set analysis are two complementary approaches for analyzing data. This paper studies approaches to constructing fuzzy concept lattices based on generalized fuzzy rough approximation operators. For a residual implicator θ satisfying θa, b) = *theta;(1 -b, 1 -a) and its dual σ, a pair of (θ,σ)-fuzzy rough approximation operators is defined. We then propose three kinds of fuzzy operators, and examine some of their basic properties. Thus, three complete fuzzy concept lattices can be produced, for which the properties are analogous to those of the classical concept lattices.

7

On Some Mathematical Structures of T-Fuzzy Rough Set Algebras in Infinite Universes of Discourse

Wu W. Z.

Fundamenta Informaticae

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2011

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Vol. 108, nr 3/4

337-369

EN

In this paper, a general framework for the study of fuzzy rough approximation operators determined by a triangular norm in infinite universes of discourse is investigated. Lower and upper approximations of fuzzy sets with respect to a fuzzy approximation space in infinite universes of discourse are first introduced. Essential properties of various types of T -fuzzy rough approximation operators are then examined. An operator-oriented characterization of fuzzy rough sets is also proposed, that is, T -fuzzy rough approximation operators are defined by axioms. Different axiom sets of upper and lower fuzzy set-theoretic operators guarantee the existence of different types of fuzzy relations which produce the same operators. A comparative study of T -fuzzy rough set algebras with some other mathematical structures are presented. It is proved that there exists a one-to-one correspondence between the set of all reflexive and T -transitive fuzzy approximation spaces and the set of all fuzzy Alexandrov spaces such that the lower and upper T -fuzzy rough approximation operators are, respectively, the fuzzy interior and closure operators. It is also shown that a reflexive fuzzy approximation space induces a measurable space such that the family of definable fuzzy sets in the fuzzy approximation space forms the fuzzy -algebra of the measurable space. Finally, it is explored that the fuzzy belief functions in the Dempster-Shafer of evidence can be interpreted by the T -fuzzy rough approximation operators in the rough set theory, that is, for any fuzzy belief structure there must exist a probability fuzzy approximation space such that the derived probabilities of the lower and upper approximations of a fuzzy set are, respectively, the T -fuzzy belief and plausibility degrees of the fuzzy set in the given fuzzy belief structure.

8

Kernelized Fuzzy Rough Sets Based Yawn Detection for Driver Fatigue Monitoring

Du Y., Chen D., Hu Q., Ma P.

Fundamenta Informaticae

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2011

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Vol. 111, nr 1

65-79

EN

Driver fatigue detection based on computer vision is considered as one of the most hopeful applications of image recognition technology. The key issue is to extract and select useful features from the driver images. In this work, we use the properties of image sequences to describe states of drivers. In addition, we introduce a kernelized fuzzy rough sets based technique to evaluate quality of candidate features and select the useful subset. Fuzzy rough sets are widely discussed in dealing with uncertainty in data analysis. We construct an algorithm for feature evaluation and selection based on fuzzy rough set model. Two classification algorithms are introduced to validate the selected features. The experimental results show the effectiveness of the proposed techniques.

9

Feature Selection via Maximizing Fuzzy Dependency

Hu Q., Zhu P., Liu J., Yang Y., Yu D.

Fundamenta Informaticae

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2010

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Vol. 98, nr 2/3

167-181

EN

Feature selection is an important preprocessing step in pattern analysis and machine learning. The key issue in feature selection is to evaluate quality of candidate features. In this work, we introduce a weighted distance learning algorithm for feature selection via maximizing fuzzy dependency. We maximize fuzzy dependency between features and decision by distance learning and then evaluate the quality of features with the learned weight vector. The features deriving great weights are considered to be useful for classification learning. We test the proposed technique with some classical methods and the experimental results show the proposed algorithm is effective.