A dynamic framework for updating approximations with increasing or decreasing objects in multi-granulation rough sets

Abstract The data we need to deal with is getting bigger and bigger in recent years, and the same happens to multi-granulation rough set, so updated schemes have been proposed with the variation of attributes or attribute values in multi-granulation rough sets, this paper puts forward a dynamic mechanism to update the approximations of multi-granulation rough sets when adding or deleting objects. Firstly, the relationships between the original approximations and updated approximations are explored when adding or deleting objects in multi-granulation rough sets, and the dynamic processes of updating optimistic and pessimistic multi-granulation rough approximations are proposed. Secondly, two corresponding dynamic algorithms are proposed to update the lower and upper approximations of optimistic and pessimistic multi-granulation rough sets. Finally, a great quantity of experiments had been implemented, and the results indicate that two dynamic algorithms proposed are more effective than the static algorithm.

Analysing diabetes using rough sets

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.2.1 ◽

2020 ◽

pp. 533-538

Author(s):

S. Arjun Raj ◽

M. Vigneshwaran

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

International Diabetes Federation ◽

Published Data ◽

In this article we use the rough set theory to generate the set of decision concepts in order to solve a medical problem.Based on officially published data by International Diabetes Federation (IDF), rough sets have been used to diagnose Diabetes.The lower and upper approximations of decision concepts and their boundary regions have been formulated here.

Computational Intelligence for Missing Data Imputation, Estimation, and Management ◽

Missing Data Estimation Using Rough Sets

10.4018/978-1-60566-336-4.ch005 ◽

2010 ◽

pp. 94-116

Author(s):

Tshilidzi Marwala

Keyword(s):

Missing Data ◽

Rough Set ◽

Rough Sets ◽

Real Data ◽

Valuable Insight ◽

Decision Tables ◽

Missing Data Estimation ◽

Data Estimation ◽

Insight Into

A number of techniques for handling missing data have been presented and implemented. Most of these proposed techniques are unnecessarily complex and, therefore, difficult to use. This chapter investigates a hot-deck data imputation method, based on rough set computations. In this chapter, characteristic relations are introduced that describe incompletely specified decision tables and then these are used for missing data estimation. It has been shown that the basic rough set idea of lower and upper approximations for incompletely specified decision tables may be defined in a variety of different ways. Empirical results obtained using real data are given and they provide a valuable insight into the problem of missing data. Missing data are predicted with an accuracy of up to 99%.

A Matrix Method for Calculation of the Approximations under the Asymmetric Similarity Relation Based Rough Sets

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.187.251 ◽

2011 ◽

Vol 187 ◽

pp. 251-256

Author(s):

Lei Wang ◽

Tian Rui Li ◽

Jun Ye

Keyword(s):

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Matrix Representation ◽

Point Of View ◽

Similarity Relation ◽

The Matrix ◽

Incomplete Information Systems ◽

Asymmetric Similarity

The essence of the rough set theory (RST) is to deal with the inconsistent problems by two definable subsets which are called the lower and upper approximations respectively. Asymmetric Similarity relation based Rough Sets (ASRS) model is one kind of extensions of the classical rough set model in incomplete information systems. In this paper, we propose a new matrix view of ASRS model and give the matrix representation of the lower and upper approximations of a concept under ASRS model. According to this matrix view, a new method is obtained for calculation of the lower and upper approximations under ASRS model. An example is given to illustrate processes of calculating the approximations of a concept based on the matrix point of view.

Generalization of Pawlak’s Approximations in Hypermodules by Set-Valued Homomorphisms

Foundations of Computing and Decision Sciences ◽

10.1515/fcds-2017-0003 ◽

2017 ◽

Vol 42 (1) ◽

pp. 59-81 ◽

Cited By ~ 1

Author(s):

Saeed Mirvakili ◽

Seid Mohammad Anvariyeh ◽

Bijan Davvaz

Keyword(s):

Rough Set ◽

Rough Sets ◽

Congruence Relation ◽

Upper Approximation ◽

Algebraic Sets ◽

Set Valued Mapping ◽

Approximation Operators ◽

Generalized Rough Set

AbstractThe initiation and majority on rough sets for algebraic hyperstructures such as hypermodules over a hyperring have been concentrated on a congruence relation. The congruence relation, however, seems to restrict the application of the generalized rough set model for algebraic sets. In this paper, in order to solve this problem, we consider the concept of set-valued homomorphism for hypermodules and we give some examples of set-valued homomorphism. In this respect, we show that every homomorphism of the hypermodules is a set-valued homomorphism. The notions of generalized lower and upper approximation operators, constructed by means of a set-valued mapping, which is a generalization of the notion of lower and upper approximations of a hypermodule, are provided. We also propose the notion of generalized lower and upper approximations with respect to a subhypermodule of a hypermodule discuss some significant properties of them.

Soft Classes and Soft Rough Classes with Applications in Decision Making

Mathematical Problems in Engineering ◽

10.1155/2016/1584528 ◽

2016 ◽

Vol 2016 ◽

pp. 1-11 ◽

Cited By ~ 13

Author(s):

Faruk Karaaslan

Keyword(s):

Decision Making ◽

Rough Set ◽

Rough Sets ◽

Soft Set ◽

Mathematical Tool ◽

Soft Sets ◽

Novel Method ◽

Rough set was defined by Pawlak in 1982. Concept of soft set was proposed as a mathematical tool to cope with uncertainty and vagueness by Molodtsov in 1999. Soft sets were combined with rough sets by Feng et al. in 2011. Feng et al. investigated relationships between a subset of initial universe of soft set and a soft set. Feng et al. defined the upper and lower approximations of a subset of initial universe over a soft set. In this study, we firstly define concept of soft class and soft class operations such as union, intersection, and complement. Then we give some properties of soft class operations. Based on definition and operations of soft classes, we define lower and upper approximations of a soft set. Subsequently, we introduce concept of soft rough class and investigate some properties of soft rough classes. Moreover, we give a novel decision making method based on soft class and present an example related to novel method.

Rough sets based on fuzzy ideals in distributive lattices

Open Mathematics ◽

10.1515/math-2020-0013 ◽

2020 ◽

Vol 18 (1) ◽

pp. 122-137

Author(s):

Yongwei Yang ◽

Kuanyun Zhu ◽

Xiaolong Xin

Keyword(s):

Distributive Lattice ◽

Rough Set ◽

Rough Sets ◽

Congruence Relation ◽

Distributive Lattices ◽

Model Based ◽

Congruence Relations ◽

Fuzzy Ideal ◽

Generalized Rough Sets

Abstract In this paper, we present a rough set model based on fuzzy ideals of distributive lattices. In fact, we consider a distributive lattice as a universal set and we apply the concept of a fuzzy ideal for definitions of the lower and upper approximations in a distributive lattice. A novel congruence relation induced by a fuzzy ideal of a distributive lattice is introduced. Moreover, we study the special properties of rough sets which can be constructed by means of the congruence relations determined by fuzzy ideals in distributive lattices. Finally, the properties of the generalized rough sets with respect to fuzzy ideals in distributive lattices are also investigated.

Rough Multisets and Information Multisystems

Advances in Decision Sciences ◽

10.1155/2011/495392 ◽

2011 ◽

Vol 2011 ◽

pp. 1-17 ◽

Cited By ~ 8

Author(s):

K. P. Girish ◽

Sunil Jacob John

Keyword(s):

Set Theory ◽

Rough Set ◽

Real World ◽

Rough Sets ◽

Rough Set Theory ◽

Types Of Information

Rough set theory uses the concept of upper and lower approximations to encapsulate inherent inconsistency in real-world objects. Information multisystems are represented using multisets instead of crisp sets. This paper begins with an overview of recent works on multisets and rough sets. Rough multiset is introduced in terms of lower and upper approximations and explores related properties. The paper concludes with an example of certain types of information multisystems.

Bi-covering rough sets

Filomat ◽

10.2298/fil2107361a ◽

2021 ◽

Vol 35 (7) ◽

pp. 2361-2369

Author(s):

Mohamed Abo-Elhamayel

Keyword(s):

Data Mining ◽

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Inclusion Relation ◽

Different Types ◽

Paper Construct ◽

The Universe

Rough set theory is a useful tool for knowledge discovery and data mining. Covering-based rough sets are important generalizations of the classical rough sets. Recently, the concept of the neighborhood has been applied to define different types of covering rough sets. In this paper, based on the notion of bi-neighborhood, four types of bi-neighborhoods related bi-covering rough sets were defined with their properties being discussed. We first show some basic properties of the introduced bi-neighborhoods. We then explore the relationships between the considered bi-covering rough sets and investigate the properties of them. Also, we show that new notions may be viewed as a generalization of the previous studies covering rough sets. Finally, figures are presented to show that the collection of all lower and upper approximations (bi-neighborhoods of all elements in the universe) introduced in this paper construct a lattice in terms of the inclusion relation ?.

Handbook of Research on Generalized and Hybrid Set Structures and Applications for Soft Computing - Advances in Computational Intelligence and Robotics ◽

Rough Approximations on Hesitant Fuzzy Sets

10.4018/978-1-4666-9798-0.ch013 ◽

2016 ◽

pp. 265-279

Author(s):

D. Deepak ◽

Sunil Jacob John

Keyword(s):

Rough Set ◽

Rough Sets ◽

Fuzzy Relation ◽

Equivalence Relations ◽

Hesitant Fuzzy Set ◽

Fuzzy Rough Sets ◽

Fuzzy Rough Set ◽

Dual Nature ◽

Fuzzy Environment ◽

Introduction of hesitant fuzzy rough sets would facilitate the use of rough set based techniques to hesitant fuzzy environment. Hesitant fuzzy rough sets deal with the lower and upper approximations in a hesitant fuzzy domain. For this purpose concepts of hesitant fuzzy relations are discussed first to create a theoretical framework to study hesitant fuzzy rough sets. The concepts of equivalence relations are discussed. Hesitant fuzzy rough sets and the properties of the approximations are discussed. The dual nature of the lower and upper approximations is proved. This chapter introduces the model of a hesitant fuzzy rough set which approximates a hesitant fuzzy set using a hesitant fuzzy relation.

Parametric Matroid of Rough Set

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488515500403 ◽

2015 ◽

Vol 23 (06) ◽

pp. 893-908 ◽

Cited By ~ 5

Author(s):

Yanfang Liu ◽

Hong Zhao ◽

William Zhu

Keyword(s):

Rough Set ◽

Equivalence Relation ◽

Rough Sets ◽

Rough Set Theory ◽

Attribute Reduction ◽

Independent Set ◽

Approximation Operator ◽

Approximation Number ◽

Lower Approximation ◽

The One

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a generalization of linear algebra and graph theory. Recently, a matroidal structure of rough sets is established and applied to the problem of attribute reduction which is an important application of rough set theory. In this paper, we propose a new matroidal structure of rough sets and call it a parametric matroid. On the one hand, for an equivalence relation on a universe, a parametric set family, with any subset of the universe as its parameter, is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore a matroid is generated, and we call it a parametric matroid of the rough set. Through the lower approximation operator, three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, partition-circuit matroids are well studied through the lower approximation number, and then we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.