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

Covering-based generalized IF rough sets with applications to multi-attribute decision-making

Attribute subset selection is an important issue in data mining and information processing. However, most automatic methodologies consider only the relevance factor between samples while ignoring the diversity factor. This may not allow the utilization value of hidden information to be exploited. For this reason, we propose a hybrid model named intuitionistic fuzzy (IF) rough set to overcome this limitation. The model combines the technical advantages of rough set and IF set and can effectively consider the above-mentioned statistical factors. First, fuzzy information granules based on IF relations are defined and used to characterize the hierarchical structures of the lower and upper approximations of IF rough set within the framework of granular computing. Then, the computation of IF rough approximations and knowledge reduction in IF information systems are investigated. Third, based on the approximations of IF rough set, significance measures are developed to evaluate the approximation quality and classification ability of IF relations. Furthermore, a forward heuristic algorithm for finding one optimal reduct of IF information systems is developed using these measures. Finally, numerical experiments are conducted on public datasets to examine the effectiveness and efficiency of the proposed algorithm in terms of the number of selected attributes, computational time, and classification accuracy.

Intuitionistic Fuzzy Rough Set-Based Granular Structures and Attribute Subset Selection

Novel fuzzy rough set models and corresponding applications to multi-criteria decision-making

With the advent of the age of big data, a typical big data set called limited labeled big data appears. It includes a small amount of labeled data and a large amount of unlabeled data. Some existing neighborhood-based rough set algorithms work well in analyzing the rough data with numerical features. But, they face three challenges: limited labeled property of big data, computational inefficiency and over-fitting in attribute reduction when dealing with limited labeled data. In order to address the three issues, a combination of neighborhood rough set and local rough set called local neighborhood rough set (LNRS) is proposed in this paper. The corresponding concept approximation and attribute reduction algorithms designed with linear time complexity can efficiently and effectively deal with limited labeled big data. The experimental results show that the proposed local neighborhood rough set and corresponding algorithms significantly outperform its original counterpart in classical neighborhood rough set. These results will enrich the local rough set theory and enlarge its application scopes.

Local neighborhood rough set

Exploring rough sets from the perspective of covering represents a promising direction in rough set theory, where concepts are approximated by substituting of an equivalent relation in classical rough set theory with a covering in covering-based rough set theory. By combining intuitionistic fuzzy (IF) β-neighborhoods induced by an IF β-covering with IF rough sets, this study develops a new rough set model, which is a generalization of the β-neighborhood fuzzy covering rough sets and IF rough sets. First, we present the concepts of IF graded covering and IF graded neighborhood, namely, IF β-covering and IF β-neighborhood, respectively. We propose an IF graded approximation space on the basis of IF graded neighborhood and discuss its uncertainty measures, namely, information entropy and rough entropy. Second, we generalize an IF rough set based on IF relation to one based on the presented IF graded neighborhood and use the distance between two IF sets to characterize the latter. Third, we present the matrix computation method for the upper and lower approximations of the presented IF rough sets based on the IF graded neighborhood. Fourth, from the multi-granulation perspective, we examine the IF graded approximation space, uncertainty measures, IF rough sets, and computation methods for its reducts. Finally, we discuss several generalizations similar to the presented IF covering rough sets.

An intuitionistic fuzzy graded covering rough set

Decision-theoretic rough set (DTRS) and multi-granulation rough set (MGRS) are two important extended types of Pawlak’s classical rough set model. The two generalized rough sets have been investigated separately by numerous researchers. However, few studies have focused on the combination of the two rough sets in intuitionistic fuzzy (IF) settings. In this study, two novel MG-IF-DTRS models, which are generalizations of MG-DTRSs, are developed by exploring DTRS and MGRS based on IF inclusion measures to explore multi-granulation IF DTRS (MG-IF-DTRS) under IF information environment. We introduce a type of inclusion measure between two IF sets and present the concept of inclusion measure-based IF-DTRS. We verify whether the model is an extension of the classical DTRS. Second, we present the inclusion measure-based optimistic and pessimistic MG-IF-DTRSs, analyze their properties, and conclude that the presented MG-IF-DTRSs are generalizations of MG-DTRSs from the viewpoint of multi-granulation. We then study the discernibility-function-based reduction methods for the presented MG-IF-DTRSs. We also provide an illustrative example of information system security audit to verify the established approach and demonstrate its validity and applicability. Finally, we discuss several possible generalizations related to MG-IF-DTRSs. This study provides a MG-IF-DTRS method for acquiring knowledge from multi-granulation IF decision systems.

Guofu Feng

Papers

An intuitionistic fuzzy graded covering rough set

Inclusion measure-based multi-granulation intuitionistic fuzzy decision-theoretic rough sets and their application to ISSA

Hierarchical structures and uncertainty measures for intuitionistic fuzzy approximation space

Dominance-based rough sets in multi-scale intuitionistic fuzzy decision tables

Double-quantitative rough sets, optimal scale selection and reduction in multi-scale dominance IF decision tables