Upper approximation of the eigenvalues of a PCO. Representation of orthogonal invariants

1965 ◽  
pp. 152-163
Author(s):  
Gaetano Fichera
Keyword(s):  
Upper Approximation

Approximate Reasoning Based on Upper Approximation

2010 ◽  
Author(s):  
Yan Lin ◽  
Mou Zhansheng ◽  
Li Fuyou ◽  
Liu Jinjin ◽  
Zhang Zidong
Keyword(s):  
Approximate Reasoning ◽  
Upper Approximation

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 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 Fuzzy covering-based rough set on two different universes and its application

2021 ◽  
Author(s):  
Bin Yang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Multiple Criteria Decision Making ◽  
Multiple Criteria ◽  
Extension Principle ◽  
Upper Approximation ◽  
New Type ◽  
New Perspective ◽  
Definition Of ◽  
Two Universes

Abstract In this paper, we propose a new type of fuzzy covering-based rough set model over two different universes by using Zadeh’s extension principle. We mainly address the following issues in this paper. First, we present the definition of fuzzy β-neighborhood, which can be seen as a fuzzy mapping from a universe to the set of fuzzy sets on another universe and study its properties. Then we define a new type of fuzzy covering-based rough set model on two different universes and investigate the properties of this model. Meanwhile, we give a necessary and sufficient condition under which two fuzzy β-coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation. Moreover, matrix representations of thefuzzy covering lower and fuzzy covering upper approximation operators are investigated. Finally, we propose a new approach to a kind of multiple criteria decision making problem based on fuzzy covering-based rough set model over two universes. The proposed models not onlyenrich the theory of fuzzy covering-based rough set but also provide a new perspective for multiple criteria decision making with uncertainty.

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