Topological characterizations of covering for special covering-based upper approximation operators

2012 ◽  
Vol 204 ◽  
pp. 70-81 ◽  
Author(s):  
Xun Ge ◽  
Xiaole Bai ◽  
Ziqiu Yun
Keyword(s):  
Upper Approximation ◽  
Approximation Operators

scholarly journals L-fuzzy upper approximation operators associated with L-generalized fuzzy remote neighborhood systems of L-fuzzy points

2020 ◽  
Vol 5 (6) ◽  
pp. 5638-5652
Author(s):  
Shoubin Sun ◽  
◽  
Lingqiang Li ◽  
Kai Hu ◽  
A. A. Ramadan ◽  
...  
Keyword(s):  
Upper Approximation ◽  
Approximation Operators

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 The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Qiao-Ling Song ◽  
Hu Zhao ◽  
Juan-Juan Zhang ◽  
A. A. Ramadan ◽  
Hong-Ying Zhang ◽  
...  
Keyword(s):  
Complete Lattice ◽  
Lattice Isomorphism ◽  
Double Negative ◽  
Lattice Structures ◽  
Fuzzy Relations ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Neighborhood System ◽  
Generalized Neighborhood System

Following the idea of L -fuzzy generalized neighborhood systems as introduced by Zhao et al., we will give the join-complete lattice structures of lower and upper approximation operators based on L -fuzzy generalized neighborhood systems. In particular, as special approximation operators based on L -fuzzy generalized neighborhood systems, we will give the complete lattice structures of lower and upper approximation operators based on L -fuzzy relations. Furthermore, if L satisfies the double negative law, then there exists an order isomorphic mapping between upper and lower approximation operators based on L -fuzzy generalized neighborhood systems; when L -fuzzy generalized neighborhood system is serial, reflexive, and transitive, there still exists an order isomorphic mapping between upper and lower approximation operators, respectively, and both lower and upper approximation operators based on L -fuzzy relations are complete lattice isomorphism.

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.

scholarly journals A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Tianyu Xue ◽  
Zhan’ao Xue ◽  
Huiru Cheng ◽  
Jie Liu ◽  
Tailong Zhu
Keyword(s):  
Rough Sets ◽  
Rough Set Theory ◽  
Binary Relations ◽  
Approximation Space ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Fuzzy Binary Relation ◽  
Novel Method ◽  
Interval Valued

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators.

Algorithms and Algorithm Analysis of Logical Difference Operation of Variable Precision Lower Approximation Operator and Grade Upper Approximation Operator

2011 ◽  
Vol 204-210 ◽  
pp. 2015-2018
Author(s):  
Xian Yong Zhang ◽  
Zhi Wen Mo ◽  
Fang Xiong
Keyword(s):  
Time Complexity ◽  
Space Complexity ◽  
Algorithm Analysis ◽  
Approximation Operator ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Variable Precision ◽  
Approximation Operators ◽  
Difference Operation

This paper aims to construct new operation of approximation operators, and explore its calculation. First it proposes logical difference operation of variable precision lower approximation operator and grade upper approximation operator. Then regular algorithm and structural algorithm are proposed and analyzed, and furthermore, a conclusion is drawn that structural algorithm has advantages in time complexity and space complexity. Finally a practical example is given to illustrate the new operation and its algorithms.

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