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AIMS Mathematics

2026, Volume 11, Issue 1: 1071-1116. doi: 10.3934/math.2026047
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Research article

Advancing smart healthcare decision-making: an innovative Fermatean fuzzy N-bipolar soft expert set framework for complex multi-criteria group evaluations

  • 1.
    Department of Mathematics, College of Science, University of Zakho, Zakho 42002, Iraq
  • 2.
    Department of Computer Science, College of Science, Cihan University-Duhok, Duhok 42001, Iraq
  • 3.
    Department of Mathematics, College of Education, University of Zakho, Zakho 42002, Iraq
  • 4.
    Department of Mathematics, Al Jumum University College, Umm Al-Qura University, Makkah, Saudi Arabia
  • 5.
    Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq
  • Published: 15 January 2026

  • MSC : 03E72, 03E75, 90B50

  • The rapid advancement of smart healthcare systems demands sophisticated mathematical tools to manage uncertainty and conflicting expert opinions in critical decision-making (DM) processes. Multi-criteria group decision making (MCGDM) plays a pivotal role in synthesizing diverse expert evaluations for complex healthcare challenges. However, existing soft set (SS) extensions often struggle to simultaneously capture multinary evaluations, bipolar reasoning, higher-order fuzzy logic, and multi-expert input. To overcome these limitations, we propose the Fermatean fuzzy N-bipolar soft expert set (FFNBSES), which enhances fuzzy representation while integrating multinary, bipolar, and multi-expert evaluations. We formally define the fundamental operations of FFNBSES and demonstrate its algebraic properties. A DM methodology based on FFNBSES is developed and applied to a healthcare case study, showcasing its superior capability to handle expert consensus and disagreement in multi-criteria evaluations. Comparative analysis within the SS theory framework highlights the enhanced flexibility and robustness of FFNBSES for real-world MCGDM problems. This work provides a powerful and comprehensive approach to support smart healthcare transformation through improved group DM under uncertainty.

    Citation: Baravan A. Asaad, Sagvan Y. Musa, Badr Alharbi, Zanyar A. Ameen. Advancing smart healthcare decision-making: an innovative Fermatean fuzzy N-bipolar soft expert set framework for complex multi-criteria group evaluations[J]. AIMS Mathematics, 2026, 11(1): 1071-1116. doi: 10.3934/math.2026047

    Related Papers:

  • The rapid advancement of smart healthcare systems demands sophisticated mathematical tools to manage uncertainty and conflicting expert opinions in critical decision-making (DM) processes. Multi-criteria group decision making (MCGDM) plays a pivotal role in synthesizing diverse expert evaluations for complex healthcare challenges. However, existing soft set (SS) extensions often struggle to simultaneously capture multinary evaluations, bipolar reasoning, higher-order fuzzy logic, and multi-expert input. To overcome these limitations, we propose the Fermatean fuzzy N-bipolar soft expert set (FFNBSES), which enhances fuzzy representation while integrating multinary, bipolar, and multi-expert evaluations. We formally define the fundamental operations of FFNBSES and demonstrate its algebraic properties. A DM methodology based on FFNBSES is developed and applied to a healthcare case study, showcasing its superior capability to handle expert consensus and disagreement in multi-criteria evaluations. Comparative analysis within the SS theory framework highlights the enhanced flexibility and robustness of FFNBSES for real-world MCGDM problems. This work provides a powerful and comprehensive approach to support smart healthcare transformation through improved group DM under uncertainty.



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