Tong-Jun Li

Fuzzy Approximation Operators Based on Coverings

This paper presents a general framework for the study of covering-based fuzzy approximation operators in which a fuzzy set can be approximated by some elements in a crisp or a fuzzy covering of the universe of discourse. Two types of approximation operators, crisp-covering-based rough fuzzy approximation operators and fuzzy-covering-based fuzzy rough approximation operators, are defined, their properties are examined in detail. Finally, the comparison of these new approximation operators is done, a sufficient and necessary condition is given under which some operators are equivalent, and approximation operator characterization of fuzzy partitions of the universe is obtained.

Intuitionistic Fuzzy Rough Approximation Operators Determined by Intuitionistic Fuzzy Triangular Norms

In this paper, relation-based intuitionistic fuzzy rough approximation operators determined by an intuitionistic fuzzy triangular norm T are investigated. By employing an intuitionistic fuzzy triangular norm T and its dual intuitionistic fuzzy triangular conorm, lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first introduced. Properties of T-intuitionistic fuzzy rough approximation operators are then examined. Relationships between special types of intuitionistic fuzzy relations and properties of T-intuitionistic fuzzy rough approximation operators are further explored.

Rough Approximations Induced by Orthocomplementations in Formal Contexts

Formal contexts is a common framework for rough set theory and formal concept analysis, and some rough set models in formal contexts have been proposed. In this paper, based on the theory of abstract approximation spaces presented by Cattaneo [1], a Brouwer orthocomplementation on the set of objects of a formal context is presented, as a result, a pair of new lower and upper rough approximation operators is introduced. Comparison between the new approximation operators and the existing approximation operators is made, and two necessary and sufficient conditions about equivalence of the operators are obtained. Relationships and algebraic structures among the definable subsets of these approximation operators are investigated.

Knowledge Spaces and Reduction of Covering Approximation Spaces

Theory of covering rough sets is one kind of effective methods for knowledge discovery. In Bonikowski covering approximation spaces, all definable sets on the universe form a knowledge space. This paper focuses on the theoretic study of knowledge spaces of covering approximation spaces. One kind of dependence relations among covering approximation spaces is introduced, the relationship between the dependence relation and lower and upper covering approximation operators are discussed in detail, and knowledge spaces of covering approximation spaces are well characterized by them. By exploring the dependence relation between a covering approximation space and its sub-spaces, the notion of the reduction of covering approximation spaces is induced, and the properties of the reductions are investigated.

Axiomatic Characterizations of Reflexive and \mathcal {T}-Transitive \mathcal {I}-Intuitionistic Fuzzy Rough Approximation Operators

Axiomatic characterizations of approximation operators are important in the study of rough set theory. In this paper, axiomatic characterizations of relation-based intuitionistic fuzzy rough approximation operators determined by an intuitionistic fuzzy implication operator (mathcal{I}) are investigated. We present a set of axioms of lower/upper (mathcal{I})-intuitionistic fuzzy set-theoretic operator which is necessary and sufficient for the existence of an intuitionistic fuzzy relation producing the same operator. We show that the lower and upper (mathcal{I})-intuitionistic fuzzy rough approximation operators generated by an arbitrary intuitionistic fuzzy relation can be described by single axioms. Moreover, the (mathcal{I})-intuitionistic fuzzy rough approximation operators generated by reflexive and (mathcal{T})-transitive intuitionistic fuzzy relations can also be characterized by single axioms.

On Dual Intuitionistic Fuzzy Rough Approximation Operators Determined by an Intuitionistic Fuzzy Implicator

In this paper, dual intuitionistic fuzzy rough approximation operators determined by an intuitionistic fuzzy implication operator

Boolean Covering Approximation Space and Its Reduction

{mathcal I}

Granule structures in formal contexts from covering rough set aspect

in infinite universes of discourse are investigated. Lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space in infinite universes of discourse are first introduced. Properties of

Rough sets and general basic set assignments

{mathcal I}

Knowledge Reduction of Incomplete Information Systems with Negative Decision Rules

-intuitionistic fuzzy rough approximation operators are then examined. Relationships between special types of intuitionistic fuzzy relations and properties of