Variable-precision-dominance-based rough set approach to interval-valued information systems

Rough set models of interval rough number information system

Classical rough set theory (RST) is based on equivalence relations, and does not have an effective mechanism when the attribute value of the objects is uncertain information. However, the information in actual problems is often uncertain, and an accurate or too vague description of the information can no longer fully meet the actual needs. Interval rough number (IRN) can reflect a certain degree of certainty in the uncertainty of the data when describing the uncertainty of the data, and can enable decision makers to make decisions more in line with actual needs according to their risk preferences. However, the current research on rough set models (RSMs) whose attribute values are interval rough numbers is still very scarce, and they cannot analyze the interval rough number information system (IRNIS) from the perspective of similar relation. therefore, three new interval rough number rough set models (IRNRSMs) based on similar relation are proposed in this paper. Firstly, aiming at the limitations of the existing interval similarity degree (ISD), new interval similarity degree and interval rough number similarity degree (IRNSD) are proposed, and their properties are discussed. Secondly, in the IRNIS, based on the newly proposed IRNSD, three IRNRSMs based on similar class, β-maximal consistent class and β-equivalent class are proposed, and their properties are discussed. And then, the relationships between these three IRNRSMs and those between their corresponding approximation accuracies are researched. Finally, it can be found that the IRNRSM based on the β-equivalent classes has the highest approximation accuracy. Proposing new IRNRSMs based on similar relation is a meaningful contribution to extending the application range of RST.

An Efficient Uncertainty Measure-based Attribute Reduction Approach for Interval-valued Data with Missing Values

Attribute reduction plays an important role in knowledge discovery and data mining. Confronted with data characterized by the interval and missing values in many data analysis tasks, it is interesting to research the attribute reduction for interval-valued data with missing values. Uncertainty measures can supply efficient viewpoints, which help us to disclose the substantive characteristics of such data. Therefore, this paper addresses the attribute reduction problem based on uncertainty measure for interval-valued data with missing values. At first, an uncertainty measure is provided for measuring candidate attributes, and then an efficient attribute reduction algorithm is developed for the interval-valued data with missing values. To improve the efficiency of attribute reduction, the objects that fall within the positive region are deleted from the whole object set in the process of selecting attributes. Finally, experimental results demonstrate that the proposed algorithm can find a subset of attributes in much shorter time than existing attribute reduction algorithms without losing the classification performance.

A Quick Algorithm for Binary Discernibility Matrix Simplification using Deterministic Finite Automata

The binary discernibility matrix, originally introduced by Felix and Ushio, is a binary matrix representation for storing discernible attributes that can distinguish different objects in decision systems. It is an effective approach for feature selection, knowledge representation and uncertainty reasoning. An original binary discernibility matrix usually contains redundant objects and attributes. These redundant objects and attributes may deteriorate the performance of feature selection and knowledge acquisition. To overcome this shortcoming, row relations and column relations in a binary discernibility matrix are defined in this paper. To compare the relationships of different rows (columns) quickly, we construct deterministic finite automata for a binary discernibility matrix. On this basis, a quick algorithm for binary discernibility matrix simplification using deterministic finite automata (BDMSDFA) is proposed. We make a comparison of BDMR (an algorithm of binary discernibility matrix reduction), IBDMR (an improved algorithm of binary discernibility matrix reduction) and BDMSDFA. Finally, theoretical analyses and experimental results indicate that the algorithm of BDMSDFA is effective and efficient.

A novel method of the generalized interval-valued fuzzy rough approximation operators

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators.

Pawlak algebra and approximate structure on fuzzy lattice

The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.