Covering-Based Variable Precision $(\mathcal {I},\mathcal {T})$-Fuzzy Rough Sets With Applications to Multiattribute Decision-Making

2019 ◽  
Vol 27 (8) ◽  
pp. 1558-1572 ◽  
Author(s):  
Haibo Jiang ◽  
Jianming Zhan ◽  
Degang Chen
Keyword(s):  
Decision Making ◽  
Rough Sets ◽  
Fuzzy Rough Sets ◽  
Variable Precision

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.

scholarly journals Double-Quantitative Generalized Multi-Granulation Set-Pair Dominance Rough Sets in Incomplete Ordered Information System

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 133
Author(s):  
Zhan-ao Xue ◽  
Min Zhang ◽  
Yong-xiang Li ◽  
Li-ping Zhao ◽  
Bing-xin Sun
Keyword(s):  
Decision Making ◽  
Information System ◽  
Rough Sets ◽  
Decision Rules ◽  
Rough Sets Theory ◽  
Quantification Method ◽  
Variable Precision ◽  
Double Quantification ◽  
Sets Theory ◽  
Variable Precision Rough Sets

Since the rough sets theory based on the double quantification method was proposed, it has attracted wide attention in decision-making. This paper studies the decision-making approach in Incomplete Ordered Information System (IOIS). Firstly, to better extract the effective information in IOIS, combined with the advantages of set-pair dominance relation and generalized multi-granulation, the generalized multi-granulation set-pair dominance variable precision rough sets (GM-SPD-VPRS) and the generalized multi-granulation set-pair dominance graded rough sets (GM-SPD-GRS) are proposed. Moreover, we discuss their related properties. Secondly, considering the GM-SPD-VPRS and the GM-SPD-GRS describe information from relative view and absolute view, respectively, we further combine the two rough sets to obtain six double-quantitative generalized multi-granulation set-pair dominance rough sets (GM-SPD-RS) models. Among them, the first two models fuse the approximation operators of two rough sets, and investigate the extreme cases of optimistic and pessimistic. The last four models combine the two rough sets by the logical disjunction operator and the logical conjunction operator. Then, we discuss relevant properties and derive the corresponding decision rules. According to the decision rules, an associated algorithm is constructed for one of the models to calculate the rough regions. Finally, we validate the effectiveness of these models with a medical example. The results indicate that the model is effective for dealing with practical problems.

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