A Neutrosophic soft topological framework for insecure intelligent decision applications

Samer R. Yaseen; Noura M. Alhouiti; Samer R. Yaseen; Noura M. Alhouiti

doi:10.3934/math.2026186

AIMS Mathematics

2026, Volume 11, Issue 2: 4596-4616. doi: 10.3934/math.2026186

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Research article

A Neutrosophic soft topological framework for insecure intelligent decision applications

Samer R. Yaseen ¹,
Noura M. Alhouiti ^{2
,
,}

1.
Department of Mathematics, College of Education for Pure Science, Tikrit University, Iraq
2.
Department of Mathematics, Faculty of Science, University of Tabuk, 71491Tabuk, Saudi Arabia

Received: 08 December 2025 Revised: 16 January 2026 Accepted: 10 February 2026 Published: 25 February 2026
MSC : 54A40, 54E55, 54D10

To enhance the reasoning ability when dealing with uncertainty, we hold that such a neutrosophic soft topological structure should be proposed. New classes of neutrosophic soft topology are developed by giving the mathematical structure, which involves min and max norm operations. In order to make a decision for options based on uncertain/or incomplete data, the model changes crucial topological concepts such as interior of set and closure into quantity indicators. The construction of the model was done applying topological operations to the truth degree, doubtfulness degree, and falsity degrees, and the decision criteria were formulated in form of neutrosophic soft sets. The frequency and reliability of decisions was measured by a decision index derived from these operations. Compared with fuzzy soft topological methods, experimental simulations further confirmed the effectiveness and robustness of the proposed model. The results indicated the potential ability of neutrosophic topology to be a universal mathematical tool used for intelligent devices operating in harsh and unpredictable surroundings.
- process decision-making,
- soft topological approach,
- intelligent devices,
- neutrosophic-soft topological model,
- mathematical entity
Citation: Samer R. Yaseen, Noura M. Alhouiti. A Neutrosophic soft topological framework for insecure intelligent decision applications[J]. AIMS Mathematics, 2026, 11(2): 4596-4616. doi: 10.3934/math.2026186

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Abstract

To enhance the reasoning ability when dealing with uncertainty, we hold that such a neutrosophic soft topological structure should be proposed. New classes of neutrosophic soft topology are developed by giving the mathematical structure, which involves min and max norm operations. In order to make a decision for options based on uncertain/or incomplete data, the model changes crucial topological concepts such as interior of set and closure into quantity indicators. The construction of the model was done applying topological operations to the truth degree, doubtfulness degree, and falsity degrees, and the decision criteria were formulated in form of neutrosophic soft sets. The frequency and reliability of decisions was measured by a decision index derived from these operations. Compared with fuzzy soft topological methods, experimental simulations further confirmed the effectiveness and robustness of the proposed model. The results indicated the potential ability of neutrosophic topology to be a universal mathematical tool used for intelligent devices operating in harsh and unpredictable surroundings.

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