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1

Knowledge Reduction in Random Incomplete Decision Tables via Evidence Theory

Wu W. Z.

Fundamenta Informaticae

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2012

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Vol. 115, nr 2/3

203-218

EN

Statisticians and database users often encounter the problem of missing or imprecise data obtained by a random experiment. Such a data set is called a random incomplete information table. In this paper, we study knowledge reduction in random incomplete information tables and random incomplete decision tables by using a hybrid model based on the rough set theory and the Dempster- Shafer theory of evidence. The concepts of random belief reducts and random plausibility reducts in random incomplete information tables and random incomplete decision tables are introduced. The relationships among the lower approximation reduct, the upper approximation reduct, the random belief reduct, the random plausibility reduct, and the classical reduct in random incomplete decision tables are examined.

2

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.

3

Attribute Reduction in Formal Contexts: A Covering Rough Set Approach

Li T-J., Wu W. Z.

Fundamenta Informaticae

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2011

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Vol. 111, nr 1

15-32

EN

This paper proposes an approach to attribute reduction in formal contexts via a covering rough set theory. The notions of reducible attributes and irreducible attributes of a formal context are first introduced and their properties are examined. Judgment theorems for determining all attribute reducts in the formal context are then obtained. According to the attribute reducts, all attributes of the formal context are further classified into three types and the characteristic of each type is characterized by the properties of irreducible classes of the formal context. Finally, by using the discernibility attribute sets, a method of distinguishing the reducible attributes and the irreducible attributes in formal contexts is presented.