scholarly journals A New Approach to Rough Set Based on Remote Neighborhood Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Shoubin Sun ◽  
Lingqiang Li ◽  
Kai Hu
Keyword(s):  
Rough Set ◽  
Topological Spaces ◽  
New Approach ◽  
Upper Approximation ◽  
Basic Properties ◽  
Approximation Operators ◽  
Dual Notion

The notion of neighborhood systems is abstracted from the geometric notion of “near”, and it is primitive in the theory of topological spaces. Now, neighborhood systems have been applied in the study of rough set by many researches. The notion of remote neighborhood systems is initial in the theory of topological molecular lattice, and it is abstracted from the geometric notion of “remote”. Therefore, the notion of remote neighborhood systems can be considered as the dual notion of neighborhood systems. In this paper, we develop a theory of rough set based on remote neighborhood systems. Precisely, we construct a pair of lower and upper approximation operators and discuss their basic properties. Furthermore, we use a set of axioms to describe the lower and upper approximation operators constructed from remote neighborhood systems.

Topological structures of a type of granule based covering rough sets

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3129-3141
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Topological Spaces ◽  
Topological Properties ◽  
Binary Relations ◽  
Upper Approximation ◽  
Approximation Operators

Rough set theory is one of important models of granular computing. Lower and upper approximation operators are two important basic concepts in rough set theory. The classical Pawlak approximation operators are based on partition and have been extended to covering approximation operators. Covering is one of the fundamental concepts in the topological theory, then topological methods are useful for studying the properties of covering approximation operators. This paper presents topological properties of a type of granular based covering approximation operators, which contains seven pairs of approximation operators. Then, topologies are induced naturally by the seven pairs of covering approximation operators, and the topologies are just the families of all definable subsets about the covering approximation operators. Binary relations are defined from the covering to present topological properties of the topological spaces, which are proved to be equivalence relations. Moreover, connectedness, countability, separation property and Lindel?f property of the topological spaces are discussed. The results are not only beneficial to obtain more properties of the pairs of covering approximation operators, but also have theoretical and actual significance to general topology.

On Characterization of Relation Based Rough Set Algebras

2010 ◽  
pp. 69-91
Author(s):  
Wei-Zhi Wu ◽  
Wen-Xiu Zhang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Axiomatic Approach ◽  
Topological Spaces ◽  
Upper Approximation ◽  
Fuzzy Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Fuzzy Topological Spaces

Rough set theory is one of the most advanced areas popularizing GrC. The basic notions in rough set theory are the lower and upper approximation operators. A rough set algebra is a set algebra with two additional lower and upper approximation operators. In this chapter, we analyze relation based rough set algebras in both crisp and fuzzy environments. We first review the constructive definitions of generalized crisp rough approximation operators, rough fuzzy approximation operators, and fuzzy rough approximation operators. We then present the essential properties of the corresponding lower and upper approximation operators. We also characterize the approximation operators by using the axiomatic approach. Finally, the connection between fuzzy rough set algebras and fuzzy topological spaces is established.

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 Comparison of Twelve Types of Rough Approximations Based on j-Neighborhood Space and j-Adhesion Neighborhood Space

2021 ◽  
Author(s):  
Mohamed Atef ◽  
Ahmed Mostafa Khalil ◽  
Abdelfatah Azzam ◽  
Abd El Fattah El Atik ◽  
Sheng Gang Li ◽  
...  
Keyword(s):  
Rough Set ◽  
Boundary Region ◽  
Previous Approach ◽  
Basic Properties ◽  
Fundamental Properties ◽  
Approximation Operators ◽  
Neighborhood Rough Set ◽  
The Relationship ◽  
Neighbor Hood

Abstract In this paper, we generalize six kinds of rough set models based on j-neighborhood space (i.e., reflexive 1 j-neighborhood rough set, reflexive 2 j-neighborhood rough set, reflexive 3 j-neighborhood rough set, similarity 4 j-neighborhood rough set, similarity 5 j-neighborhood rough set, and similarity 6 j-neighbor\\hood rough set), and investigate some of their basic properties. Further, we propose a new neighborhood space called j-adhesion neighborhood based on six types of rough set models (i.e., reflexive 7 j-adhesion neighborhood rough set, reflexive 8 j-adhesion neighborhood rough set, reflexive 9 j-adhesion neighborhood rough set, similarity 10 j-adhesion neighborhood rough set, similarity 11 j-adhesion neighborhood rough set, and similarity 12 j-neighbor\\hood rough set) to reduce the boundary region and the accuracy. The fundamental properties of approximation operators based on j-adhesion neighborhood space are investigated. The relationship between the properties of these types is explained. Finally, we give comparisons between the proposed approach with the previous approach (i.e., Abo-Tabl's approach and Dai et al.'s approach) from six types of rough set models. Consequently, the accuracy from the proposed approach is improved.

scholarly journals Topological properties of a pair of relation-based approximation operators

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6175-6183
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Topological Properties ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Basic Concepts

Rough set theory is an important tool for data mining. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough approximation operators are based on equivalence relations and have been extended to relation-based generalized rough approximation operators. This paper presents topological properties of a pair of relation-based generalized rough approximation operators. A topology is induced by the pair of generalized rough approximation operators from an inverse serial relation. Then, connectedness, countability, separation property and Lindel?f property of the topological space are discussed. The results are not only beneficial to obtain more properties of the pair of approximation operators, but also have theoretical and actual significance to general topology.

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.

Comparison of six types of rough approximations based on j-neighborhood space and j-adhesion neighborhood space

2020 ◽  
Vol 39 (3) ◽  
pp. 4515-4531 ◽  
Author(s):  
Mohammed Atef ◽  
Ahmed Mostafa Khalil ◽  
Sheng-Gang Li ◽  
A.A. Azzam ◽  
Abd El Fattah El Atik
Keyword(s):  
Rough Set ◽  
Basic Properties ◽  
Fundamental Properties ◽  
Approximation Operators ◽  
Neighborhood Rough Set ◽  
Type 3 ◽  
The Relationship

In this paper, we generalize three types of rough set models based on j-neighborhood space (i.e, type 1 j-neighborhood rough set, type 2 j-neighborhood rough set, and type 3 j-neighborhood rough set), and investigate some of their basic properties. Also, we present another three types of rough set models based on j-adhesion neighborhood space (i.e, type 4 j-adhesion neighborhood rough set, type 5 j-adhesion neighborhood rough set, and type 6 j-adhesion neighborhood rough set). The fundamental properties of approximation operators based on j-adhesion neighborhood space are established. The relationship between the properties of these types is explained. Finally, according to j-adhesion neighborhood space, we give a comparison between the Yao’s approach and our approach.

scholarly journals A New Single-Valued Neutrosophic Rough Sets and Related Topology

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Qiu Jin ◽  
Kai Hu ◽  
Chunxin Bo ◽  
Lingqiang Li
Keyword(s):  
Rough Sets ◽  
Topological Spaces ◽  
Approximation Operator ◽  
Approximation Space ◽  
Fuzzy Rough Sets ◽  
Approximation Spaces ◽  
Lower Approximation ◽  
Basic Properties ◽  
Approximation Operators ◽  
New Type

(Fuzzy) rough sets are closely related to (fuzzy) topologies. Neutrosophic rough sets and neutrosophic topologies are extensions of (fuzzy) rough sets and (fuzzy) topologies, respectively. In this paper, a new type of neutrosophic rough sets is presented, and the basic properties and the relationships to neutrosophic topology are discussed. The main results include the following: (1) For a single-valued neutrosophic approximation space U , R , a pair of approximation operators called the upper and lower ordinary single-valued neutrosophic approximation operators are defined and their properties are discussed. Then the further properties of the proposed approximation operators corresponding to reflexive (transitive) single-valued neutrosophic approximation space are explored. (2) It is verified that the single-valued neutrosophic approximation spaces and the ordinary single-valued neutrosophic topological spaces can be interrelated to each other through our defined lower approximation operator. Particularly, there is a one-to-one correspondence between reflexive, transitive single-valued neutrosophic approximation spaces and quasidiscrete ordinary single-valued neutrosophic topological spaces.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Evidence Theory ◽  
Topological Spaces ◽  
Relative Significance ◽  
Approximation Operators ◽  
Covering Rough Set

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.

scholarly journals Further Study of MultigranulationT-Fuzzy Rough Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Wentao Li ◽  
Xiaoyan Zhang ◽  
Wenxin Sun
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Approximation Space ◽  
Fuzzy Rough Sets ◽  
Fuzzy Rough Set ◽  
Upper Approximation ◽  
Fuzzy Approximation ◽  
Approximation Operators ◽  
Special Instance

The optimistic multigranulationT-fuzzy rough set model was established based on multiple granulations underT-fuzzy approximation space by Xu et al., 2012. From the reference, a natural idea is to consider pessimistic multigranulation model inT-fuzzy approximation space. So, in this paper, the main objective is to make further studies according to Xu et al., 2012. The optimistic multigranulationT-fuzzy rough set model is improved deeply by investigating some further properties. And a complete multigranulationT-fuzzy rough set model is constituted by addressing the pessimistic multigranulationT-fuzzy rough set. The full important properties of multigranulationT-fuzzy lower and upper approximation operators are also presented. Moreover, relationships between multigranulation and classicalT-fuzzy rough sets have been studied carefully. From the relationships, we can find that theT-fuzzy rough set model is a special instance of the two new types of models. In order to interpret and illustrate optimistic and pessimistic multigranulationT-fuzzy rough set models, a case is considered, which is helpful for applying these theories to practical issues.

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