Ju-Sheng Mi

Attribute reduction in fuzzy decision formal contexts

The classical concept lattices express the precise relation between object sets and attribute sets, but fuzzy concept lattices express the uncertain relation between object sets and attribute sets. Therefore, it is important to study hierarchy fuzzy knowledge from a fuzzy formal context. In this paper, a kind of fuzzy decision formal context is proposed and (α, β) reduct based on this fuzzy decision formal context is defined. Furthermore, we propose a method to judge attribute consistent sets and reducts in fuzzy decision formal contexts. Finally, a Boolean method is also formulated to attribute reduction in fuzzy decision formal context from the view of the discernibility matrix.

Attribute reduction based on maximal rules in decision formal context

AbstractOne of the key issues in the theory of concept lattices is to extract the useful rules from the decision formal context. The maximal rules implicate the others, thus people are interested in them. This paper proposes two new kinds of attribute reduction in the decision formal context based on maximal rules. The reducts preserve all the condition extensions and the decision extensions related to the original maximal rules. The internal relationship between the original maximal rules and the maximal rules in the reduced decision formal context is derived. The reducts can make the maximal rules more concise and accurate. The mathematical property of the proposed attribute reduction is investigated and we construct the discernibility matrix and function to compute all the reducts. Finally, all the attributes are classified into three types based on the maximal rules. The characteristics of these types of attributes are also analyzed.

On the use of cut set for attribute reduction in L-fuzzy concept lattice

Concept lattice is an effective tool for knowledge discovery and has been applied to many fields successfully. The objects and attributes have clear relations in the classical formal context, but there are a lot of fuzzy information in real-life applications. Therefore, it is important to study the fuzzy formal context. As we know, the fuzzy set and the classical set can be transformed into each other based on the cut set. Thus, it is believed that the cut set can be used in the research of fuzzy concept lattice. In this paper, a preliminary exploration to use the cut set is carried out. In particular, the cut set is employed to construct the discernibility matrix of L-fuzzy formal context and then all the reducts can be obtained via the use of discernibility function. After that, all the attributes are classified into three types by their significances in constructing the L-fuzzy concept lattice. The characteristics of these types of attributes are also analyzed. The obtained results in this paper are beneficial for the research of fuzzy formal context based on the cut set in further.

Inclusion measure and similarity measure of intuitionistic fuzzy sets

This paper introduces a new definition of intuitionistic fuzzy (IF for short) inclusion measure. Five kinds of IF inclusion measure are constructed by means of different operators especially by IF implicator. It is shown that the similarity measure between two IF sets obtained from IF inclusion measure hold properties of normal similarity measure.

MEASURING INCLUSION, SIMILARITY AND COMPATIBILITY BETWEEN ATANASSOV'S INTUITIONISTIC FUZZY SETS

This paper establishes an axiomatic definition of inclusion measures between Atanassovs intuitionistic fuzzy (A-IF for short) sets. Some kinds of A-IF inclusion measures are constructed by different A-IF operators especially by A-IF implicator, and some new methods for measuring the degree of similarity between A-IF sets are proposed. Moreover, the similarity measure obtained from an A-IF inclusion measure satisfies properties of normal similarity measure. We then define a compatibility measure by a predicates logical idea and construct several functions to measure compatibility for an intuitionistic t-norm.

Intuitionistic fuzzy topology space based on fuzzy rough sets

In this paper, we mainly study the relationship between IF rough approximation operators and IF topological spaces. First, we discuss IF topologies generated by IF approximation space and IF approximation space generated by IF topologies. Then we discuss the relationship between IF topologies generated by IF approximation space and IF approximation space generated by IF topologies. Finally, we study the properties of the IF cover approximation space.

Entropy and similarity measure of intuitionistic fuzzy sets

In this paper, a new kind of entropy and a similarity measure of intuitionistic fuzzy sets are proposed, and the relationships between the entropy and similarity measure are examined in detail. It is proved that similarity measure and entropy of intuitionistic fuzzy sets can be transformed by each other based on their axiomatic definitions.

The Minimal Sets of Axioms Characterizing Rough Fuzzy Approximation Operators

Axiomatic characterization of rough approximation operators is one of the important aspects in the study of rough set theory. In axiomatic approach, various classes of rough approximation operators are characterized by different sets of axioms. Axioms of approximation operators guarantee the existence of certain types of binary relations producing the same operators. In this paper, the approximation operators determined by a triangular norm are studied, the independence of axioms characterizing rough fuzzy approximation operators is examined, and then the minimal sets of axioms for the characterization of fuzzy approximation operators are presented

Boundary region based rough sets

Rough sets are mainly defined by means of neighborhood systems. In this paper, a type of novel definition of the approximation operators is proposed via a predefined boundary region based on a binary relation. Then, the comparison between the new definitions and the original ones is made. The necessary and sufficient conditions of their equipollence are obtained. This paper also gives the definitions of boundaries based on covering. By employing the boundaries, a type of novel definition of the approximation operators based on covering is proposed. It is shown that the novel operators are equivalent to a type of covering approximation operators. Finally, with the aid of the boundary region, the relation between the general binary relations and the covering-based approximation operators is examined.

A novel approach for ranking in interval-valued information systems

In decision making analysis, ranking decision with anti-noise capability is a very desirable issue. This paper focuses on analysing data in interval-valued information systems. A new approach ranking with weighted standardized cardinality (WSC) and inclusion indicator in interval-valued information systems is proposed. It is a novel generalization of ranking method based on dominance classes. The new approach overcomes the drawback of sensitivity to noise for raking using dominance classes-based method. In this paper, each object with all attribute values is regarded as an interval-valued fuzzy set (IVF-set). By defining WSC with controlling parameters and single interval inclusion indicator, two kinds of inclusion indicators of the IVF-set are constructed. The approach is based on the novel idea of raking with WSC and inclusion indicator rather than dominance classes. Experiments verify that the new approach is noise-resistant.