Yanhui Zhai

Generating complete set of implications for formal contexts

In this paper, a necessary and sufficient condition on which a set of implications is complete is proposed with the help of the notion of model from logic. Besides, using the closure of an attribute subset to a set of implications, we present a formal method to remove the redundant implications from a complete set. Subsequently, we provide an algorithm to generate a complete set of implications and an illustrative example guarantees the availability of the algorithm.

A model for type-2 fuzzy rough sets

Rough set theory is an important approach to granular computing. Type-1 fuzzy set theory permits the gradual assessment of the memberships of elements in a set. Hybridization of these assessments results in a fuzzy rough set theory. Type-2 fuzzy sets possess many advantages over type-1 fuzzy sets because their membership functions are themselves fuzzy, which makes it possible to model and minimize the effects of uncertainty in type-1 fuzzy logic systems. Existing definitions of type-2 fuzzy rough sets are based on vertical-slice or α-plane representations of type-2 fuzzy sets, and the granular structure of type-2 fuzzy rough sets has not been discussed. In this paper, a definition of type-2 fuzzy rough sets based on a wavy-slice representation of type-2 fuzzy sets is given. Then the concepts of granular type-2 fuzzy sets are proposed, and their properties are investigated. Finally, granular type-2 fuzzy sets are used to describe the granular structures of the lower and upper approximations of a type-2 fuzzy set, and an example of attribute reduction is given.

Decision implication canonical basis

Due to its special role on logical deduction and practical applications of attribute implications, canonical basis has attracted much attention and been widely studied in Formal Concept Analysis. Canonical basis is constructed on pseudo-intents and, as an attribute implication basis, possesses of many important features, such as completeness, non-redundancy and minimality among all complete sets of attribute implications. In this paper, to deduce an analogous basis for decision implications, we introduce the notion of decision premise and form the so-called decision implication canonical basis. Furthermore, we show that the basis is complete, non-redundant and minimal among all complete sets of decision implications. We also present an algorithm to generate this canonical basis and analyze time complexity of this algorithm. Introduce the notions of decision premise and decision implication canonical basis.Show that the canonical basis is complete, non-redundant and minimal.Present an algorithm to generate this canonical basis.

Incremental entropy-based clustering on categorical data streams with concept drift

Clustering on categorical data streams is a relatively new field that has not received as much attention as static data and numerical data streams. One of the main difficulties in categorical data analysis is lacking in an appropriate way to define the similarity or dissimilarity measure on data. In this paper, we propose three dissimilarity measures: a point-cluster dissimilarity measure (based on incremental entropy), a cluster-cluster dissimilarity measure (based on incremental entropy) and a dissimilarity measure between two cluster distributions (based on sample standard deviation). We then propose an integrated framework for clustering categorical data streams with three algorithms: Minimal Dissimilarity Data Labeling (MDDL), Concept Drift Detection (CDD) and Cluster Evolving Analysis (CEA). We also make comparisons with other algorithms on several data streams synthesized from real data sets. Experiments show that the proposed algorithms are more effective in generating clustering results and detecting concept drift.

A novel attribute reduction approach for multi-label data based on rough set theory

Multi-label classification is an active research field in machine learning. Because of the high dimensionality of multi-label data, attribute reduction (also known as feature selection) is often necessary to improve multi-label classification performance. Rough set theory has been widely used for attribute reduction with much success. However, little work has been done on applying rough set theory to attribute reduction in multi-label classification. In this paper, a novel attribute reduction method based on rough set theory is proposed for multi-label data. First, the uncertainties conveyed by labels are analyzed, and a new type of attribute reduct is introduced, called complementary decision reduct. The relationships between complementary decision reduct and two representative types of attribute reducts are also investigated, showing significant advantages of complementary decision reduct in revealing the uncertainties implied in multi-label data. Second, a discernibility matrix-based approach is introduced for computing all complementary decision reducts, and a heuristic algorithm is proposed for effectively computing a single complementary decision reduct. Experiments on real-life data demonstrate that the proposed approach can effectively reduce unnecessary attributes and improve multi-label classification accuracy.

Granular Structure of Type-2 Fuzzy Rough Sets over Two Universes

Granular structure plays a very important role in the model construction, theoretical analysis and algorithm design of a granular computing method. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In classical rough set theory, equivalence classes are basic granules, and the lower and upper approximations of a set can be computed by those basic granules. In the theory of fuzzy rough set, granular fuzzy sets can be used to describe the lower and upper approximations of a fuzzy set. This paper discusses the granular structure of type-2 fuzzy rough sets over two universes. Definitions of type-2 fuzzy rough sets over two universes are given based on a wavy-slice representation of type-2 fuzzy sets. Two granular type-2 fuzzy sets are deduced and then proven to be basic granules of type-2 fuzzy rough sets over two universes. Then, the properties of lower and upper approximation operators and these two granular type-2 fuzzy sets are investigated. At last, several examples are given to show the applications of type-2 fuzzy rough sets over two universes.

A Variable Precision Attribute Reduction Approach in Multilabel Decision Tables

Owing to the high dimensionality of multilabel data, feature selection in multilabel learning will be necessary in order to reduce the redundant features and improve the performance of multilabel classification. Rough set theory, as a valid mathematical tool for data analysis, has been widely applied to feature selection (also called attribute reduction). In this study, we propose a variable precision attribute reduct for multilabel data based on rough set theory, called δ-confidence reduct, which can correctly capture the uncertainty implied among labels. Furthermore, judgement theory and discernibility matrix associated with δ-confidence reduct are also introduced, from which we can obtain the approach to knowledge reduction in multilabel decision tables.

Fuzzy decision implication canonical basis

Fuzzy decision implication (FDI) is regarded as a basic form of knowledge representation in fuzzy decision based formal concept analysis. How to reduce redundant FDIs and generate an informative and minimal set of FDIs from a given set of FDIs is the main concern in the study of FDI. This paper introduces fuzzy decision premise, constructs fuzzy decision implication canonical basis (FD canonical basis) and proves that FD canonical basis is complete, non-redundant and optimal, i.e., FD canonical basis contains the least number of FDIs among all complete sets of FDIs. Thus, from a given set of FDIs, one can generate its corresponding FD canonical basis, which turns out to be informative (complete) and minimal (optimal).

Variable decision knowledge representation: A logical description

Abstract Decision-making is important in all science-based professions, where specialists apply their knowledge to making valuable decisions. In Formal Concept Analysis, decision-making problem is handled within decision contexts and in the form of decision implications. In this paper, we introduce the notion of variable decision implication to generalize decision implications and uncertain decision implications. We describe the semantic aspect of variable decision implications by defining the notions of follow , non-redundant , complete , etc., and provide the syntactical description by presenting three inference rules and proving their soundness and completeness. This paper also provides a re-explanation of deduction of associative rules, and should be regarded as a starting point for effectively reducing the size of associative rules.

Group decision making based on vague preference relations

Vague sets, characterized by a truth-membership function and a false-membership function, was introduced by Gau and Buehrer [1]. In this paper, we define the concepts of vague preference relation and incomplete vague preference relation. Approaches to group decision making based on vague preference relations and based on incomplete vague preference relations respectively are proposed. Then, the vague arithmetic averaging operator and vague weighted arithmetic averaging operator are used to aggregate vague preference information. The ranking method proposed is applied to ranking and selection of alternatives. Finally, by a numerical example, we illustrate the proposed approach.