Structure of Upper and Lower Approximation Spaces of Infinite Sets

2002 ◽  
pp. 461-473 ◽  
Author(s):  
D. S. Malik ◽  
John N. Mordeson
Keyword(s):  
Approximation Spaces ◽  
Lower Approximation ◽  
Infinite Sets

scholarly journals Idealization of j-approximation spaces

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 287-301
Author(s):  
Mona Hosny
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Current Work ◽  
Core Concept ◽  
Approximation Spaces ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Generalized Rough Set ◽  
The Ideal

The current work concentrates on generating different topologies by using the concept of the ideal. These topologies are used to make more thorough studies on generalized rough set theory. The rough set theory was first proposed by Pawlak in 1982. Its core concept is upper and lower approximations. The principal goal of the rough set theory is reducing the vagueness of a concept to uncertainty areas at their borders by increasing the lower approximation and decreasing the upper approximation. For the mentioned goal, different methods based on ideals are proposed to achieve this aim. These methods are more accurate than the previous methods. Hence it is very interesting in rough set context for removing the vagueness (uncertainty).

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.

Computable numberings of families of infinite sets

2019 ◽  
Vol 58 (3) ◽  
pp. 334-343
Author(s):  
M. V. Dorzhieva
Keyword(s):  
Computable Numberings ◽  
Infinite Sets

Soft sets and soft topology on nearness approximation spaces

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4117-4125 ◽  
Author(s):  
Hatice Tasbozan ◽  
Ilhan Icen ◽  
Nurettin Bagirmaz ◽  
Abdullah Ozcan
Keyword(s):  
Soft Sets ◽  
Approximation Spaces ◽  
Soft Topology

scholarly journals Parametric Matroid of Rough Set

2015 ◽  
Vol 23 (06) ◽  
pp. 893-908 ◽  
Author(s):  
Yanfang Liu ◽  
Hong Zhao ◽  
William Zhu
Keyword(s):  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Independent Set ◽  
Approximation Operator ◽  
Approximation Number ◽  
Lower Approximation ◽  
The One

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a generalization of linear algebra and graph theory. Recently, a matroidal structure of rough sets is established and applied to the problem of attribute reduction which is an important application of rough set theory. In this paper, we propose a new matroidal structure of rough sets and call it a parametric matroid. On the one hand, for an equivalence relation on a universe, a parametric set family, with any subset of the universe as its parameter, is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore a matroid is generated, and we call it a parametric matroid of the rough set. Through the lower approximation operator, three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, partition-circuit matroids are well studied through the lower approximation number, and then we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.

scholarly journals Non-repetitive colorings of infinite sets

2003 ◽  
Vol 265 (1-3) ◽  
pp. 365-373 ◽  
Author(s):  
Jarosław Grytczuk ◽  
Wiesław Śliwa
Keyword(s):  
Infinite Sets
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