Interpretations of belief functions in approximation operators by covering

The rough set theory and the evidence theory are two important methods used to deal with uncertainty. The relationships between the rough set theory and the evidence theory have been discussed. In covering rough set theory, several pairs of covering approximation operators are characterized by belief and plausibility functions. The purpose of this paper is to review and examine interpretations of belief functions in covering approximation operators. Firstly, properties of the belief structures induced by two pairs of covering approximation operators are presented. Then, for a belief structure with the properties, there exists a probability space with a covering such that the belief and plausibility functions defined by the given belief structure are, respectively, the belief and plausibility functions induced by one of the two pairs of covering approximation operators. Moreover, two necessary and sufficient conditions for a belief structure to be the belief structure induced by one of the two pairs of covering approximation operators are presented.

Covering Rough Set Based Incremental Feature Selection for Mixed Decision System

Covering rough sets conceptualize different types of features with their respective generated coverings. By integrating these coverings into a single covering, covering rough set based feature selection finds valuable features from a mixed decision system with symbolic, real-valued, missing-valued, and set-valued features. Existing approaches to covering rough set based feature selection, however, are intractable to handle large mixed data. Therefore, an efficient strategy of incremental feature selection is proposed by presenting a mixed data set in sample subsets one after another. Once a new sample subset comes in, the relative discernible relation of each feature is updated to disclose incremental feature selection scheme that decides the strategies of increasing informative features and removing redundant features. The incremental scheme is applied to establish two incremental feature selection algorithms from large or dynamic mixed datasets. The first algorithm updates the feature subset upon the sequent arrival of sample subsets, and returns the reduct when no further sample subsets are obtained. The second one merely updates the relative discernible relations, and finds the reduct when no subsets are obtained. Extensive experiments demonstrate that the two proposed incremental algorithms, especially the second one speeds up covering rough set based feature selection without sacrificing too much classification performance.

On Some Types of Multigranulation Covering Based on Binary Relations

Recently, the notions of right and left covering rough sets were constructed by right and left neighborhoods to propose four types of multigranulation covering rough set (MGCRS) models. These models were constructed using the granulations as equivalence relations. In this paper, we introduce four types of multigranulation covering rough set models under arbitrary relations using the q -minimal and q -maximal descriptors of objects in a given universe. We also study the properties of these new models. Thus, we explore the relationships between these models. Then, we put forward an algorithm to illustrate the method of reduction based on the presented model. Finally, we give an illustrative example to show its efficiency and importance.

On Different Types of Single-Valued Neutrosophic Covering Rough Set with Application in Decision-Making

This paper aims to propose the notion of Type-1 single-valued neutrosophic complementary β -neighborhood (briefly, Type-1 SVN complementary β -neighborhood) and use it to introduce a novel class of 1-single-valued neutrosophic β -covering rough set (briefly, 1-SVN β -CRS). Then, we will merge the 1-SVN β -neighborhood and 1-SVN complementary β -neighborhood to create new two models of 1-SVN β -CRS. Furthermore, we will discuss the relationships between the present work and Wang and Zhang’s work. For further study on Type-2 Wang and Zhang’s models, we will define the 2-SVN complementary β -neighborhood and use it to present a novel class of 2-SVN β -CRS. Also, we combine the 2-SVN β -neighborhood and 2-SVN complementary β -neighborhood to investigate the new two models of 2-SVN β -CRS. Lately, we will demonstrate two illustrative examples as real problems to show the differences between two of our approaches and Wang and Zhang’s approach.

Numerical Characterizations of Topological Reductions of Covering Information Systems in Evidence Theory

The reductions of covering information systems in terms of covering approximation operators are one of the most important applications of covering rough set theory. Based on the connections between the theory of topology and the covering rough set theory, two kinds of topological reductions of covering information systems are discussed in this paper, which are characterized by the belief and plausibility functions from the evidence theory. The topological spaces by two pairs of covering approximation operators in covering information systems are pseudo-discrete, which deduce partitions. Then, using plausibility function values of the sets in the partitions, the definitions of significance and relative significance of coverings are presented. Hence, topological reduction algorithms based on the evidence theory are proposed in covering information systems, and an example is adopted to illustrate the validity of the algorithms.

Attribute reduction in fuzzy multi-covering decision systems via observational- consistency and fuzzy discernibility

Fuzzy covering rough set model is a popular and important theoretical tool for computation of uncertainty, and provides an effective approach for attribute reduction. However, attribute reductions derived directly from fuzzy lower or upper approximations actually still occupy large of redundant information, which leads to a lower ratio of attribute-reduced. This paper introduces a kind of parametric observation sets on the approximations, and further proposes so called parametric observational-consistency, which is applied to attribute reduction in fuzzy multi-covering decision systems. Then the related discernibility matrix is developed to provide a way of attribute reduction. In addition, for multiple observational parameters, this article also introduces a recursive method to gradually construct the multiple discernibility matrix by composing the refined discernibility matrix and incremental discernibility matrix based on previous ones. In such case, an attribute reduction algorithm is proposed. Finally, experiments are used to demonstrate the feasibility and effectiveness of our proposed method.