A topological-lattice similarity measure for information systems

Mateb O. Aljabri; Abdelfattah A. El-Atik; Ahmed Zedan; Mateb O. Aljabri; Abdelfattah A. El-Atik; Ahmed Zedan

doi:10.3934/math.20261261

AIMS Mathematics

2026, Volume 11, Issue 9: 32081-32108. doi: 10.3934/math.20261261

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Research article

A topological-lattice similarity measure for information systems

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: 12 July 2026 Revised: 29 August 2026 Accepted: 08 September 2026 Published: 29 September 2026
MSC : 03E75, 06A06, 06B23, 54A05

In this paper, a topological framework induced by information systems is developed and investigated. The associated topological spaces are constructed through attribute-based relations, and their fundamental topological properties are examined. Based on these topological representations, a similarity-based framework is developed to quantify and analyze the degrees of similarity among objects in an information system. The proposed measure captures structural characteristics through topological concepts such as neighborhoods, closures, and open sets. To further enhance the analysis, lattice structures associated with the generated topologies are employed to reveal hierarchical relationships and provide an additional perspective for similarity assessment. Furthermore, an attribute reduction procedure is proposed to identify and eliminate redundant attributes while preserving the essential information contained in the system. The proposed method provides a theoretical framework for attribute reduction based on topological and lattice structures and is illustrated through a representative information-system example. The obtained results show that the integration of topological spaces and lattice structures provides a robust and efficient framework for measuring similarity between information systems, supporting data reduction, information analysis, and decision-making applications.
- topological spaces,
- similarity matrices,
- information system,
- lattice theory,
- rough set
Citation: Mateb O. Aljabri, Abdelfattah A. El-Atik, Ahmed Zedan. A topological-lattice similarity measure for information systems[J]. AIMS Mathematics, 2026, 11(9): 32081-32108. doi: 10.3934/math.20261261

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Abstract

In this paper, a topological framework induced by information systems is developed and investigated. The associated topological spaces are constructed through attribute-based relations, and their fundamental topological properties are examined. Based on these topological representations, a similarity-based framework is developed to quantify and analyze the degrees of similarity among objects in an information system. The proposed measure captures structural characteristics through topological concepts such as neighborhoods, closures, and open sets. To further enhance the analysis, lattice structures associated with the generated topologies are employed to reveal hierarchical relationships and provide an additional perspective for similarity assessment. Furthermore, an attribute reduction procedure is proposed to identify and eliminate redundant attributes while preserving the essential information contained in the system. The proposed method provides a theoretical framework for attribute reduction based on topological and lattice structures and is illustrated through a representative information-system example. The obtained results show that the integration of topological spaces and lattice structures provides a robust and efficient framework for measuring similarity between information systems, supporting data reduction, information analysis, and decision-making applications.

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