scholarly journals Matroidal Structure of Generalized Rough Sets Based on Tolerance Relations

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Hui Li ◽  
Yanfang Liu ◽  
William Zhu
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Matroid Theory ◽  
Upper Approximation ◽  
Tolerance Relation ◽  
The Family ◽  
Generalized Rough Set ◽  
The Relationship ◽  
Generalized Rough Sets

Rough set theory provides an effective tool to deal with uncertain, granular, and incomplete knowledge in information systems. Matroid theory generalizes the linear independence in vector spaces and has many applications in diverse fields, such as combinatorial optimization and rough sets. In this paper, we construct a matroidal structure of the generalized rough set based on a tolerance relation. First, a family of sets are constructed through the lower approximation of a tolerance relation and they are proved to satisfy the circuit axioms of matroids. Thus we establish a matroid with the family of sets as its circuits. Second, we study the properties of the matroid including the base and the rank function. Moreover, we investigate the relationship between the upper approximation operator based on a tolerance relation and the closure operator of the matroid induced by the tolerance relation. Finally, from a tolerance relation, we can get a matroid of the generalized rough set based on the tolerance relation. The matroid can also induce a new relation. We investigate the connection between the original tolerance relation and the induced relation.

scholarly journals Covering-Based Rough Sets on Eulerian Matroids

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bin Yang ◽  
Ziqiong Lin ◽  
William Zhu
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Closure Operator ◽  
Matroid Theory ◽  
Upper Approximation ◽  
Significant Generalization ◽  
Eulerian Matroid ◽  
Vital Structure

Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Covering-based rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensively from linear algebra and graph theory. In this paper, one type of covering-based approximations is studied from the viewpoint of Eulerian matroids. First, we explore the circuits of an Eulerian matroid from the perspective of coverings. Second, this type of covering-based approximations is represented by the circuits of Eulerian matroids. Moreover, the conditions under which the covering-based upper approximation operator is the closure operator of a matroid are presented. Finally, a matroidal structure of covering-based rough sets is constructed. These results show many potential connections between covering-based rough sets and matroids.

Model of Covering Rough Sets in the Machine Intelligence

2012 ◽  
Vol 548 ◽  
pp. 735-739
Author(s):  
Hong Mei Nie ◽  
Jia Qing Zhou
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Machine Intelligence ◽  
Upper Approximation ◽  
Generalized Rough Sets

Rough set theory has been proposed by Pawlak as a useful tool for dealing with the vagueness and granularity in information systems. Classical rough set theory is based on equivalence relation. The covering rough sets are an improvement of Pawlak rough set to deal with complex practical problems which the latter one can not handle. This paper studies covering-based generalized rough sets. In this setting, we investigate common properties of classical lower and upper approximation operations hold for the covering-based lower and upper approximation operations and relationships among some type of covering rough sets.

A New Description of Transversal Matroids Through Rough Set Approach

2021 ◽  
Vol 179 (4) ◽  
pp. 399-416
Author(s):  
Zhaohao Wang
Keyword(s):  
Rough Set ◽  
Rough Set Theory ◽  
Sufficient Conditions ◽  
Mining Machine ◽  
Matroid Theory ◽  
Approximation Number ◽  
Upper Approximation ◽  
Transversal Matroid ◽  
Necessary And Sufficient ◽  
The Relationship

Matroid theory is a useful tool for the combinatorial optimization issue in data mining, machine learning and knowledge discovery. Recently, combining matroid theory with rough sets is becoming interesting. In this paper, rough set approaches are used to investigate an important class of matroids, transversal matroids. We first extend the concept of upper approximation number functions in rough set theory and propose the notion of generalized upper approximation number functions on a set system. By means of the new notion, we give some necessary and sufficient conditions for a subset to be a partial transversal of a set system. Furthermore, we obtain a new description of a transversal matroid by the generalized upper approximation number function. We show that a transversal matroid can be induced by the generalized upper approximation number function which can be decomposed into the sum of some elementary generalized upper approximation number functions. Conversely, we also prove that a generalized upper approximation number function can induce a transversal matroid. Finally, we apply the generalized upper approximation number function to study the relationship among transversal matroids.

scholarly journals Reduction of Neighborhood-Based Generalized Rough Sets

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Zhaohao Wang ◽  
Lan Shu ◽  
Xiuyong Ding
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Open Problems ◽  
The Third ◽  
Generalized Rough Sets

Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. This paper discusses five types of existing neighborhood-based generalized rough sets. The concepts of minimal neighborhood description and maximal neighborhood description of an element are defined, and by means of the two concepts, the properties and structures of the third and the fourth types of neighborhood-based rough sets are deeply explored. Furthermore, we systematically study the covering reduction of the third and the fourth types of neighborhood-based rough sets in terms of the two concepts. Finally, two open problems proposed by Yun et al. (2011) are solved.

ON ATTRIBUTE REDUCTION WITH INTUITIONISTIC FUZZY ROUGH SETS

2012 ◽  
Vol 20 (01) ◽  
pp. 59-76 ◽  
Author(s):  
ZHIMING ZHANG ◽  
JINGFENG TIAN
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Theoretical Foundation ◽  
Attribute Reduction ◽  
Upper Approximation ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Rough Sets ◽  
Axiomatic Approaches

Intuitionistic fuzzy (IF) rough sets are the generalization of traditional rough sets obtained by combining the IF set theory and the rough set theory. The existing research on IF rough sets mainly concentrates on the establishment of lower and upper approximation operators using constructive and axiomatic approaches. Less effort has been put on the attribute reduction of databases based on IF rough sets. This paper systematically studies attribute reduction based on IF rough sets. Firstly, attribute reduction with traditional rough sets and some concepts of IF rough sets are reviewed. Then, we introduce some concepts and theorems of attribute reduction with IF rough sets, and completely investigate the structure of attribute reduction. Employing the discernibility matrix approach, an algorithm to find all attribute reductions is also presented. Finally, an example is proposed to illustrate our idea and method. Altogether, these findings lay a solid theoretical foundation for attribute reduction based on IF rough sets.

scholarly journals Soft Covering Based Rough Sets and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Şaziye Yüksel ◽  
Zehra Güzel Ergül ◽  
Naime Tozlu
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Prostate Cancer Risk ◽  
Approximation Operator ◽  
Soft Sets ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Model Combining ◽  
Rough Approximation ◽  
Generalized Rough Set

Soft rough sets which are a hybrid model combining rough sets with soft sets are defined by using soft rough approximation operators. Soft rough sets can be seen as a generalized rough set model based on soft sets. The present paper aims to combine the covering soft set with rough set, which gives rise to the new kind of soft rough sets. Based on the covering soft sets, we establish soft covering approximation space and soft covering rough approximation operators and present their basic properties. We show that a new type of the soft covering upper approximation operator is smaller than soft upper approximation operator. Also we present an example in medicine which aims to find the patients with high prostate cancer risk. Our data are 78 patients from Selçuk University Meram Medicine Faculty.

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

2017 ◽  
Vol 42 (1) ◽  
pp. 59-81 ◽  
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 ◽  
Lower And Upper Approximations ◽  
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.

Uncertainty Measurement for Covering Rough Sets

2014 ◽  
Vol 22 (02) ◽  
pp. 217-233 ◽  
Author(s):  
Jianhua Dai ◽  
Debiao Huang ◽  
Huashi Su ◽  
Haowei Tian ◽  
Tian Yang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Accuracy Measure ◽  
Uncertainty Measurement ◽  
Covering Rough Set ◽  
Measure Entropy ◽  
Theoretical Results ◽  
Generalized Rough Sets

Covering rough set theory is an important generalization of traditional rough set theory. So far, the studies on covering generalized rough sets mainly focus on constructing different types of approximation operations. However, little attention has been paid to uncertainty measurement in covering cases. In this paper, a new kind of partial order is proposed for coverings which is used to evaluate the uncertainty measures. Consequently, we study uncertain measures like roughness measure, accuracy measure, entropy and granularity for covering rough set models which are defined by neighborhoods and friends. Some theoretical results are obtained and investigated.

scholarly journals Rough Sets Data Analysis in Knowledge Discovery: A Case of Kuwaiti Diabetic Children Patients

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Aboul ella Hassanien ◽  
Mohamed E. Abdelhafez ◽  
Hala S. Own
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Confusion Matrix ◽  
Decision Rules ◽  
Minimal Subset ◽  
Discretization Algorithm ◽  
Diabetic Children ◽  
The Relationship ◽  
Accuracy Rates

The main goal of this study is to investigate the relationship between psychosocial variables and diabetic children patients and to obtain a classifier function with which it was possible to classify the patients on the basis of assessed adherence level. The rough set theory is used to identify the most important attributes and to induce decision rules from 302 samples of Kuwaiti diabetic children patients aged 7–13 years old. To increase the efficiency of the classification process, rough sets with Boolean reasoning discretization algorithm is introduced to discretize the data, then the rough set reduction technique is applied to find all reducts of the data which contains the minimal subset of attributes that are associated with a class label for classification. Finally, the rough sets dependency rules are generated directly from all generated reducts. Rough confusion matrix is used to evaluate the performance of the predicted reducts and classes. A comparison between the obtained results using rough sets with decision tree, neural networks, and statistical discriminate analysis classifier algorithms has been made. Rough sets show a higher overall accuracy rates and generate more compact rules.

scholarly journals Idealization of j-approximation spaces

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 287-301
Author(s):  
Mona Hosny
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Current Work ◽  
Core Concept ◽  
Approximation Spaces ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Generalized Rough Set ◽  
The Ideal

The current work concentrates on generating different topologies by using the concept of the ideal. These topologies are used to make more thorough studies on generalized rough set theory. The rough set theory was first proposed by Pawlak in 1982. Its core concept is upper and lower approximations. The principal goal of the rough set theory is reducing the vagueness of a concept to uncertainty areas at their borders by increasing the lower approximation and decreasing the upper approximation. For the mentioned goal, different methods based on ideals are proposed to achieve this aim. These methods are more accurate than the previous methods. Hence it is very interesting in rough set context for removing the vagueness (uncertainty).

Sign in / Sign up

Export Citation Format

Share Document