scholarly journals Certain Types of Covering-Based Multigranulation ( ℐ , T )-Fuzzy Rough Sets with Application to Decision-Making

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Jue Ma ◽  
Mohammed Atef ◽  
Shokry Nada ◽  
Ashraf Nawar
Keyword(s):  
Decision Making ◽  
Rough Sets ◽  
Fuzzy Rough Sets ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Numerical Example ◽  
Variable Precision ◽  
The Family

As a generalization of Zhan’s method (i.e., to increase the lower approximation and decrease the upper approximation), the present paper aims to define the family of complementary fuzzy β -neighborhoods and thus three kinds of covering-based multigranulation ( ℐ , T )-fuzzy rough sets models are established. Their axiomatic properties are investigated. Also, six kinds of covering-based variable precision multigranulation ( ℐ , T )-fuzzy rough sets are defined and some of their properties are studied. Furthermore, the relationships among our given types are discussed. Finally, a decision-making algorithm is presented based on the proposed operations and illustrates with a numerical example to describe its performance.

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.

Certain types of fuzzy soft β-covering based fuzzy rough sets with application to decision-making

2021 ◽  
pp. 1-12
Author(s):  
Ashraf S. Nawar ◽  
Mohammed Atef ◽  
Ahmed Mostafa Khalil
Keyword(s):  
Decision Making ◽  
Rough Sets ◽  
Fuzzy Rough Sets ◽  
Numerical Example ◽  
Lower And Upper Approximations

The aim of this paper is to introduce and study different kinds of fuzzy soft β-neighborhoods called fuzzy soft β-adhesion neighborhoods and to analyze some of their properties. Further, the concepts of soft β-adhesion neighborhoods are investigated and the related properties are studied. Then, we present new kinds of lower and upper approximations by means of different fuzzy soft β-neighborhoods. The relationships among our models (i.e., Definitions 3.9, 3.12, 3.15 and 3.18) and Zhang models [48] are also discussed. Finally, we construct an algorithm based on Definition 3.12, when k = 1 to solve the decision-making problems and illustrate its applicability through a numerical example.

The Rough Linear Approximate Space and Soft Linear Space

2016 ◽  
Vol 25 (2) ◽  
pp. 251-261
Author(s):  
Yingcang Ma ◽  
Shaoyang Li ◽  
Yamei Liu
Keyword(s):  
Boolean Algebra ◽  
Linear Space ◽  
Linear Algebra ◽  
Rough Sets ◽  
Linear Subspace ◽  
Real Life ◽  
Inclusion Relation ◽  
Soft Sets ◽  
Lower Approximation ◽  
Upper Approximation

AbstractThe studies of rough sets and soft sets, which can deal with uncertain problems in real life, have developed rapidly in recent years. We have known that linear space is a very important concept in linear algebra, so the aim of this paper was mainly focused on combining research in linear space, rough sets, and soft sets. First, according to the properties of upper (lower) approximation in rough linear space, the inclusion relation of the upper approximation’s union and the inclusion relation of the lower approximation’s intersection are improved. The equations of the upper approximation’s union and the lower approximation’s intersection are given. Secondly, the connection of linear space to rough sets is explored and the rough linear approximate space is proposed, which is proved to be a Boolean algebra under the intersection, union, and complementary operators. Thirdly, the combination of linear space and soft set is discussed, the definitions of soft linear space and soft linear subspace are proposed, and their properties are explored. Finally, the definitions of lower and upper approximation of a subspace X in soft linear space are given and their properties are studied. These investigations would enrich the studies of linear space, soft sets, and rough sets.

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