Huaxiong Li

Relative reducts in consistent and inconsistent decision tables of the Pawlak rough set model

A relative reduct can be considered as a minimum set of attributes that preserves a certain classification property. This paper investigates three different classification properties, and suggests three distinct definitions accordingly. In the Pawlak rough set model, while the three definitions yield the same set of relative reducts in consistent decision tables, they may result in different sets in inconsistent tables. Relative reduct construction can be carried out based on a discernibility matrix. The study explicitly stresses a fact, that the definition of a discernibility matrix should be tied to a certain property. Regarding the three classification properties, we can define three distinct definitions accordingly. Based on the common structure of the specific definitions of relative reducts and discernibility matrices, general definitions of relative reducts and discernibility matrices are suggested.

Sequential three-way decision and granulation for cost-sensitive face recognition

Many previous studies on face recognition attempted to seek a precise classifier to achieve a low misclassification error, which is based on an assumption that all misclassification costs are the same. In many real-world scenarios, however, this assumption is not reasonable due to the imbalanced misclassification cost and insufficient high-quality facial image information. To address this issue, we propose a sequential three-way decision method for cost-sensitive face recognition. The proposed method is based on a formal description of granular computing. It develops a sequential strategy in a decision process. In each decision step, it seeks a decision which minimizes the misclassification cost rather than misclassification error, and it incorporates the boundary decision into the decision set such that a delayed decision can be made if available high-quality facial image information is insufficient for a precise decision. To describe the granular information of the facial image in three-way decision steps, we develop a series of image granulation methods based on two-dimensional subspace projection methods including 2DPCA, 2DLDA and 2DLPP. The sequential three-way decisions and granulation methods present an applicable simulation on human decisions in face recognition, which simulate a sequential decision strategy from rough granule to precise granule. The experiments were conducted on two popular facial image database, which validated the effectiveness of the proposed methods.

A Multiple-category Classification Approach with Decision-theoretic Rough Sets

By considering the levels of tolerance for errors and the cost of actions in real decision procedure, a new two-stage approach is proposed to solve the multiple-category classification problems with Decision-Theoretic Rough Sets (DTRS). The first stage is to change an m-category classification problem (m > 2) into an m two-category classification problem, and form three types of decision regions: positive region, boundary region and negative region with different states and actions by using DTRS. The positive region makes a decision of acceptance, the negative region makes a decision of rejection, and the boundary region makes a decision of abstaining. The second stage is to choose the best candidate classification in the positive region by using the minimum probability error criterion with Bayesian discriminant analysis approach. A case study of medical diagnosis demonstrates the proposed method.

Intuitionistic fuzzy multigranulation rough sets

Abstract Exploring rough sets from the perspective of multigranulation represents a promising direction in rough set theory, where concepts are approximated by multiple granular structures represented by binary relations. Through a combination of multigranulation rough sets with intuitionistic fuzzy rough sets, this study develops a new multigranulation rough set model, called an intuitionistic fuzzy multigranulation rough set (IFMGRS). In the multigranulation framework, three types of IFMGRSs that are generalizations of three existing intuitionistic fuzzy rough set models are proposed. First, we present three types of IFMGRSs. From their basic properties, we conclude that they are extensions of three existing intuitionistic fuzzy rough sets. Second, we define the reducts of the three types of IFMGRSs to eliminate redundant intuitionistic fuzzy granulations. Third, we examine the reduction approaches of IFMGRS with a detailed example and discuss the general reduction theory of IFMGRS.

Attribute reduction in decision-theoretic rough set model: a further investigation

The monotonicity of positive region in PRS (Pawlak Rough Set) and DTRS (Decision-Theoretic Rough Set) are comparatively discussed in this paper. Theoretic analysis shows that the positive region in DTRS model may expand with the decrease of the attributes, which is essentially different from that of PRS model and leads to a new definition of attribute reduction in DTRS model. A heuristic algorithm for the newly defined attribute reduction in DTRS model is proposed, in which the positive region is allowed to expand instead of remaining unchanged in the process of deleting attributes. Results of experimental analysis are included to validate the theoretic analysis and quantify the effectiveness of the proposed attribute reduction algorithm.

A Multi-View Decision Model Based on Decision-Theoretic Rough Set

A review of Pawlak rough set models and probabilistic rough set models is presented, and a multi-view decision method based on decision-theoretic rough set model is proposed, in which optimistic decision, pessimistic decision, and indifferent decision are provided according to the cost of misclassification, which are well interpreted based on both practical examples and theoretic analysis.

Cost-sensitive sequential three-way decision modeling using a deep neural network

A DNN-based sequential three-way decision for image data analysis is proposed.A cost-sensitive decision strategy is presented to balance two kinds of costs.The granular features are extracted based on different iterations of training DNN.The method presents a simulation on human decisions from rough to precise granular. Three-way decision (3WD) models have been widely investigated in the fields of approximate reasoning and decision making. Recently, sequential 3WD models have attracted increasing interest, especially for image data analysis. It is essential to select an appropriate feature extraction and granulation method for sequential 3WD-based image data analysis. Among the existing feature extraction methods, deep neural networks (DNNs) have been considered widely due to their powerful capacity for representation. However, several important problems affect the application of DNN-based feature extraction methods to sequential 3WD. First, it takes a long time for a DNN to obtain an optimal feature representation. Second, most DNN algorithms are cost-blind methods and they assume that the costs of all misclassifications are the same, which is not the case in real-world scenarios. Third, DNN algorithms are two-way decision models and they cannot provide boundary decisions if sufficient information is not available. To address these problems, we propose a DNN-based sequential granular feature extraction method, which sequentially extracts a hierarchical granular structure from the input images. Based on the sequential multi-level granular features, a cost-sensitive sequential 3WD strategy is presented that considers the misclassification cost and test cost in different decision phases. Our experimental analysis validated the effectiveness of the proposed sequential DNN-based feature extraction method for 3WD.

Non-Monotonic Attribute Reduction in Decision-Theoretic Rough Sets

For most attribute reduction in Pawlak rough set model PRS, monotonicity is a basic property for the quantitative measure of an attribute set. Based on the monotonicity, a series of attribute reductions in Pawlak rough set model such as positive-region-preserved reductions and condition entropy-preserved reductions are defined and the corresponding heuristic algorithms are proposed in previous rough sets research. However, some quantitative measures of attribute set may be non-monotonic in probabilistic rough set model such as decision-theoretic rough set DTRS, and the non-monotonic definition of the attribute reduction should be reinvestigated and the heuristic algorithm should be reconsidered. In this paper, the monotonicity of the positive region in PRS and DTRS are comparatively discussed. Theoretic analysis shows that the positive region in DTRS model may be expanded with the decrease of the attributes, which is essentially different from that in PRS model. Hereby, a new non-monotonic attribute reduction is presented for the DTRS model in this paper, and a heuristic algorithm for searching the newly defined attribute reduction is proposed, in which the positive region is allowed to be expanded instead of remaining unchanged in the process of attribute reduction. Experimental analysis is included to validate the theoretic analysis and quantify the effectiveness of the proposed attribute reduction algorithm.

Cost-Sensitive classification based on decision-theoretic rough set model

A framework of cost-sensitive classification based on decision-theoretic rough set model is proposed to determine the local minimum total cost classification and the local optimal test attributes set. Based on the proposed classification strategy, a cost-sensitive classification algorithm CSDTRS is presented. CSDTRS focuses on searching for an optimal test attributes set with minimum total cost including both misclassification cost and test cost, and then determine the classification based on the optimal test attributes set. A heuristic function for evaluating the attribute is presented to determine which attribute should be added in the optimal test attributes set. Experiments on four UCI data sets are performed to show the effectiveness of the proposed classification algorithm.

Cost-Sensitive Three-Way Decision: A Sequential Strategy

Three-way decision model is an extension of two-way decision model, in which boundary region decision is regarded as a new feasible decision choice when precise decision can not be immediately made due to lack of available information. In this paper, a cost-sensitive sequential three-way decision model is presented, which simulate a gradual decision process from rough granule to precise granule. At the beginning of the sequential decision process, the decision results have a high decision cost and many instances are decided as boundary region due to lack of information. With the increasing of the decision steps, the decision cost decrease and more instances are precisely decided. Eventually the decision cost achieve at a satisfying value and the boundary region disappears. The paper presents both theoretic analysis and experimental validation on this proposed model.