Strengthening the digital fortress: A Pythagorean fuzzy Dombi–Archimedean approach to network security decisions

Haitham Qawaqneh; Abdallah Shihadeh; Wael Mahmoud Mohammad Salameh; Walid Abdelfattah; Ikhtesham Ullah; Arif Mehmood; Jamil J. Hamja; Celine Tali Malabong

doi:10.46481/jnsps.2026.3617

Authors

Haitham Qawaqneh
Department of Basic Science, Al-Zaytoonah University of Jordan, Amman 11733, Jordan
Abdallah Shihadeh
Department of Mathematics, Faculty of Science, The Hashemite University, Zarqa 13133, PO box 330127, Jordan
Wael Mahmoud Mohammad Salameh
Faculty of Information Technology, Abu Dhabi University, Abu Dhabi, United Arab Emirates
Walid Abdelfattah
[email protected]

Humanities and Social Research Center, Northern Border University, Arar, Saudi Arabia
Ikhtesham Ullah
Department of Mathematics, Abbottabad University of Science and Technology, Havelian, Pakistan
Arif Mehmood
Institute of Numerical Sciences, Gomal University, Dera Ismail Khan, Pakistan
Jamil J. Hamja
Department of Mathematics, College of Mathematical Sciences, Mindanao State University–Tawi-Tawi College of Technology and Oceanography, 7500 Tawi-Tawi, Philippines
Celine Tali Malabong
MSU TCTO Sitangkai Community High School, Secondary Education Department, Mindanao State University Tawi-Tawi College of Technology and Oceanography, 7500 Tawi-Tawi, Philippines

Keywords:

Pythagorean fuzzy set, Dombi operator, Archimedean operator, Network security, Multi-criteria decision making

Abstract

Network-security planning frequently depends on judgments that are imprecise, incomplete, and sometimes internally conflicting. Conventional numerical decision models are effective when assessments are available in exact form; however, they are less expressive when experts must report both supporting and opposing evidence for the same security alternative. This paper develops a Pythagorean fuzzy Dombi--Archimedean aggregation framework for multi-criteria decision making under such conditions. In the proposed model, each expert assessment is represented as a Pythagorean fuzzy number and is aggregated through Dombi-type flexibility functions embedded in an Archimedean operational structure. Within this unified notation, weighted averaging, ordered weighted averaging, hybrid averaging, weighted geometric, ordered weighted geometric, and hybrid geometric operators are introduced. The main algebraic properties of these operators, including closure, idempotency, boundedness, and monotonicity, are established from the operational laws with explicit admissibility requirements. A network-security case study is then presented to rank six candidate security systems with respect to four risk-oriented criteria. The numerical implementation includes tabular computations, a procedural flowchart, sensitivity analysis with respect to the flexibility parameter, and a comparative ranking discussion. The results show that the proposed framework offers a coherent and adjustable mechanism for ranking security alternatives when the available decision information involves hesitation, conflict, and expert uncertainty.

Dimensions

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