Interval-valued Pythagorean fuzzy Aczel–Alsina Hamy mean operators for multi-attribute group decision-making with smart healthcare application

Amjid Khan; Jawad Ali; Suhad Ali Osman Abdallah; Ioan-Lucian Popa; Amjid Khan; Jawad Ali; Suhad Ali Osman Abdallah; Ioan-Lucian Popa

doi:10.3934/math.20261300

AIMS Mathematics

2026, Volume 11, Issue 10: 33183-33237. doi: 10.3934/math.20261300

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Research article

Interval-valued Pythagorean fuzzy Aczel–Alsina Hamy mean operators for multi-attribute group decision-making with smart healthcare application

1.
Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat 26000, KPK, Pakistan
2.
School of Computer and Artificial Intelligence, Shandong Jianzhu University, Ji'nan 250101, China
3.
Computational Intelligence Center Shandong Jianzhu University No.1000, Fengming Road, Lingang Development Zone, Ji'nan 250101, China
4.
Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
5.
Department of Computing, Mathematics and Electronics, "1 Decembrie 1918" University of Alba Iulia, Alba Iulia 510009, Romania
6.
Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, Brasov 500091, Romania

Received: 02 May 2026 Revised: 07 July 2026 Accepted: 13 July 2026 Published: 13 October 2026
MSC : 03E72, 68T35, 90B50

Selecting optimal smart healthcare systems is a complex multi-attribute group decision-making (MAGDM) problem characterized by multiple conflicting criteria and inherent uncertainty in expert judgments. Traditional approaches often struggle to adequately model intercriteria relationships and flexible information aggregation under such vagueness. This paper develops a novel MAGDM framework based on interval-valued Pythagorean fuzzy sets (IVPFSs). To effectively aggregate uncertain information, several new aggregation operators are proposed by integrating Aczel–Alsina (AA) operations with the Hamy mean and its dual form. The fundamental mathematical properties of these operators, including idempotency, monotonicity, and boundedness, are rigorously established. A systematic MAGDM methodology is constructed using the proposed operators, where criteria weights are objectively determined using the measurement of alternatives and ranking according to compromise solution (MEREC) method. Its practicality and effectiveness are demonstrated through a real-world case study on smart healthcare system selection. Sensitivity analysis confirms the stability of the ranking results with respect to the AA and Hamy mean parameters. Comparative analysis with existing methods further highlights the superiority of the proposed approach in capturing intercriteria dependencies and providing more balanced and reliable rankings.
- interval-valued Pythagorean fuzzy sets,
- Aczel–Alsina norm,
- Hamy mean operators,
- group decision-making,
- smart healthcare system selection
Citation: Amjid Khan, Jawad Ali, Suhad Ali Osman Abdallah, Ioan-Lucian Popa. Interval-valued Pythagorean fuzzy Aczel–Alsina Hamy mean operators for multi-attribute group decision-making with smart healthcare application[J]. AIMS Mathematics, 2026, 11(10): 33183-33237. doi: 10.3934/math.20261300

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Abstract

Selecting optimal smart healthcare systems is a complex multi-attribute group decision-making (MAGDM) problem characterized by multiple conflicting criteria and inherent uncertainty in expert judgments. Traditional approaches often struggle to adequately model intercriteria relationships and flexible information aggregation under such vagueness. This paper develops a novel MAGDM framework based on interval-valued Pythagorean fuzzy sets (IVPFSs). To effectively aggregate uncertain information, several new aggregation operators are proposed by integrating Aczel–Alsina (AA) operations with the Hamy mean and its dual form. The fundamental mathematical properties of these operators, including idempotency, monotonicity, and boundedness, are rigorously established. A systematic MAGDM methodology is constructed using the proposed operators, where criteria weights are objectively determined using the measurement of alternatives and ranking according to compromise solution (MEREC) method. Its practicality and effectiveness are demonstrated through a real-world case study on smart healthcare system selection. Sensitivity analysis confirms the stability of the ranking results with respect to the AA and Hamy mean parameters. Comparative analysis with existing methods further highlights the superiority of the proposed approach in capturing intercriteria dependencies and providing more balanced and reliable rankings.

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