Generating topologies for attribute-value tables using lattices and neighborhoods

Musaed M. Alreshidi; Abdelfattah A. El-Atik; Ahmed Zedan; Musaed M. Alreshidi; Abdelfattah A. El-Atik; Ahmed Zedan

doi:10.3934/math.2026896

AIMS Mathematics

2026, Volume 11, Issue 7: 22133-22149. doi: 10.3934/math.2026896

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Research article

Generating topologies for attribute-value tables using lattices and neighborhoods

1.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
2.
Department of Mathematics, Faculty of Science, Aswan University, Aswan 81528, Egypt

Received: 22 May 2026 Revised: 28 June 2026 Accepted: 08 July 2026 Published: 24 July 2026
MSC : 54D05, 54F15, 54F50, 37B10

The values in information tables are responsible for dividing the objects of space into partition of object space, which may be topologically. This partition forms a base for topology in complete information system and a subbase for incomplete information systems depending on the arrangement data. The values in information system are responsible for generated different topologies according to the relationship between objects and attributes, since the value is the connection between them. The effectiveness of values in information tables is that the values generate the equivalence classes for a Pawlak approximation space in complete information system, where every equivalence class is a subset of objects and has the same properties. Moreover, attribute values are the primary method for forming these equivalence classes of the approximation space, and the collecting data may take a lot of time, money, and power. If the data does not provide a good analysis, then the effort is wasted and we lose money and time. Therefore, we want to benefit of the data, and change the type of values into another form to generalize of the approximate space. The main aim of this paper was to solve some problems related to values in information system tables by unimportant data reduction due to the structure and types of topologies. On the other hand, the formation of objects lattice for space elements through topological concepts was used. In the new approximation space, the undefinable rough sets changed into definable rough sets depending on new equivalence classes for a Pawlak approximation space through changing the values in information table.
- neighborhood,
- topological spaces,
- rough set theory,
- information system
Citation: Musaed M. Alreshidi, Abdelfattah A. El-Atik, Ahmed Zedan. Generating topologies for attribute-value tables using lattices and neighborhoods[J]. AIMS Mathematics, 2026, 11(7): 22133-22149. doi: 10.3934/math.2026896

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Abstract

The values in information tables are responsible for dividing the objects of space into partition of object space, which may be topologically. This partition forms a base for topology in complete information system and a subbase for incomplete information systems depending on the arrangement data. The values in information system are responsible for generated different topologies according to the relationship between objects and attributes, since the value is the connection between them. The effectiveness of values in information tables is that the values generate the equivalence classes for a Pawlak approximation space in complete information system, where every equivalence class is a subset of objects and has the same properties. Moreover, attribute values are the primary method for forming these equivalence classes of the approximation space, and the collecting data may take a lot of time, money, and power. If the data does not provide a good analysis, then the effort is wasted and we lose money and time. Therefore, we want to benefit of the data, and change the type of values into another form to generalize of the approximate space. The main aim of this paper was to solve some problems related to values in information system tables by unimportant data reduction due to the structure and types of topologies. On the other hand, the formation of objects lattice for space elements through topological concepts was used. In the new approximation space, the undefinable rough sets changed into definable rough sets depending on new equivalence classes for a Pawlak approximation space through changing the values in information table.

References

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