Topological properties of locally finite covering rough sets and K-topological rough set structures

2021 ◽  
Vol 25 (10) ◽  
pp. 6865-6877
Author(s):  
Sang-Eon Han
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Topological Properties ◽  
Finite Covering ◽  
Locally Finite

Topological Properties of Multigranular Rough sets on Fuzzy Approximation Spaces

2019 ◽  
Vol 6 (2) ◽  
pp. 1-18
Author(s):  
B.K. Tripathy ◽  
Suvendu Kumar Parida ◽  
Sudam Charan Parida
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Topological Properties ◽  
Approximation Spaces ◽  
Fuzzy Approximation ◽  
Accuracy Measure ◽  
Multiple Granularity ◽  
The Universe ◽  
Single Relation ◽  
Proximity Relation

One of the extensions of the basic rough set model introduced by Pawlak in 1982 is the notion of rough sets on fuzzy approximation spaces. It is based upon a fuzzy proximity relation defined over a Universe. As is well known, an equivalence relation provides a granularization of the universe on which it is defined. However, a single relation defines only single granularization and as such to handle multiple granularity over a universe simultaneously, two notions of multigranulations have been introduced. These are the optimistic and pessimistic multigranulation. The notion of multigranulation over fuzzy approximation spaces were introduced recently in 2018. Topological properties of rough sets are an important characteristic, which along with accuracy measure forms the two facets of rough set application as mentioned by Pawlak. In this article, the authors introduce the concept of topological property of multigranular rough sets on fuzzy approximation spaces and study its properties.

scholarly journals Characterizations of an MW-topological rough set structure

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2357-2366
Author(s):  
Sang-Eon Han
Keyword(s):  
Euclidean Space ◽  
Compact Subset ◽  
Rough Set ◽  
Dimensional Euclidean Space ◽  
Finite Covering ◽  
Locally Finite ◽  
Target Set ◽  
The Universe

Regarding the study of digital topological rough set structures, the present paper explores some mathematical and systemical structures of the Marcus-Wyse (MW-, for brevity) topological rough set structures induced by the locally finite covering approximation (LFC-, for brevity) space (R2,C) (see Proposition 3.4 in this paper), where R2 is the 2-dimensional Euclidean space. More precisely, given the LFC-space (R2,C), based on the set of adhesions of points in R2 inducing certain LFC-rough concept approximations, we systematically investigate various properties of the MW-topological rough concept approximations (D -M, D+M) derived from this LFC-space (R2,C). These approaches can facilitate the study of an estimation of roughness in terms of an MW-topological rough set. In the present paper each of a universe U and a target set X(? U) need not be finite and further, a covering C is locally finite. In addition, when regarding both an M-rough set and an MW-topological rough set in Sections 3, 4, and 5, the universe U(? R2) is assumed to be the set R2 or a compact subset of R2 or a certain set containing the union of all adhesions of x ? X (see Remark 3.6).

Analysing diabetes using rough sets

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 ◽  
Lower And Upper Approximations

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.

scholarly journals Parametric Matroid of Rough Set

2015 ◽  
Vol 23 (06) ◽  
pp. 893-908 ◽  
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.

GENERALIZED FUZZY ROUGH SETS BY CONDITIONAL PROBABILITY RELATIONS

2002 ◽  
Vol 16 (07) ◽  
pp. 865-881 ◽  
Author(s):  
ROLLY INTAN ◽  
MASAO MUKAIDONO
Keyword(s):  
Conditional Probability ◽  
Rough Set ◽  
Real World ◽  
Rough Sets ◽  
Similarity Relation ◽  
Fuzzy Rough Set ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
Real World Applications ◽  
The Universe

In 1982, Pawlak proposed the concept of rough sets with a practical purpose of representing indiscernibility of elements or objects in the presence of information systems. Even if it is easy to analyze, the rough set theory built on a partition induced by equivalence relation may not provide a realistic view of relationships between elements in real-world applications. Here, coverings of, or nonequivalence relations on, the universe can be considered to represent a more realistic model instead of a partition in which a generalized model of rough sets was proposed. In this paper, first a weak fuzzy similarity relation is introduced as a more realistic relation in representing the relationship between two elements of data in real-world applications. Fuzzy conditional probability relation is considered as a concrete example of the weak fuzzy similarity relation. Coverings of the universe is provided by fuzzy conditional probability relations. Generalized concepts of rough approximations and rough membership functions are proposed and defined based on coverings of the universe. Such generalization is considered as a kind of fuzzy rough set. A more generalized fuzzy rough set approximation of a given fuzzy set is proposed and discussed as an alternative to provide interval-value fuzzy sets. Their properties are examined.

scholarly journals On Some Types of Covering-Based ℐ , T -Fuzzy Rough Sets and Their Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Mohammed Atef ◽  
José Carlos R. Alcantud ◽  
Hussain AlSalman ◽  
Abdu Gumaei
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Practical Application ◽  
Fuzzy Rough Sets ◽  
Fuzzy Rough Set ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Numerical Example ◽  
Variable Precision

The notions of the fuzzy β -minimal and maximal descriptions were established by Yang et al. (Yang and Hu, 2016 and 2019). Recently, Zhang et al. (Zhang et al. 2019) presented the fuzzy covering via ℐ , T -fuzzy rough set model ( FC ℐ T FRS ), and Jiang et al. (Jiang et al., in 2019) introduced the covering through variable precision ℐ , T -fuzzy rough sets ( CVP ℐ T FRS ). To generalize these models in (Jiang et al., 2019 and Zhang et al. 2019), that is, to improve the lower approximation and reduce the upper approximation, the present paper constructs eight novel models of an FC ℐ T FRS based on fuzzy β -minimal (maximal) descriptions. Characterizations of these models are discussed. Further, eight types of CVP ℐ T FRS are introduced, and we investigate the related properties. Relationships among these models are also proposed. Finally, we illustrate the above study with a numerical example that also describes its practical application.

Data Clustering Algorithms Using Rough Sets

2013 ◽  
pp. 297-327 ◽  
Author(s):  
B.K. Tripathy ◽  
Adhir Ghosh
Keyword(s):  
Comparative Study ◽  
Rough Set ◽  
Fuzzy Clustering ◽  
Fuzzy Set ◽  
Rough Sets ◽  
Data Clustering ◽  
Clustering Algorithms ◽  
Clustering Methods ◽  
Future Studies ◽  
Multiple Clusters

Developing Data Clustering algorithms have been pursued by researchers since the introduction of k-means algorithm (Macqueen 1967; Lloyd 1982). These algorithms were subsequently modified to handle categorical data. In order to handle the situations where objects can have memberships in multiple clusters, fuzzy clustering and rough clustering methods were introduced (Lingras et al 2003, 2004a). There are many extensions of these initial algorithms (Lingras et al 2004b; Lingras 2007; Mitra 2004; Peters 2006, 2007). The MMR algorithm (Parmar et al 2007), its extensions (Tripathy et al 2009, 2011a, 2011b) and the MADE algorithm (Herawan et al 2010) use rough set techniques for clustering. In this chapter, the authors focus on rough set based clustering algorithms and provide a comparative study of all the fuzzy set based and rough set based clustering algorithms in terms of their efficiency. They also present problems for future studies in the direction of the topics covered.

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