Complex Pythagorean Fuzzy Aczel–Alsina Weighted Heronian Mean Operators and Their Applications in MCDM

Javeria Gul; Hua Zhu; Bushra Naz; Ziad Khan; Rashid Jan; Fawad Hussain; Imran Qureshi

doi:10.31181/sor202778

Authors

Javeria Gul Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan Author https://orcid.org/0000-0002-5397-7435
Hua Zhu School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan, China Author https://orcid.org/0000-0003-0238-0580
Bushra Naz Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan Author https://orcid.org/0009-0008-5492-4184
Ziad Khan Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan Author https://orcid.org/0000-0003-1834-9545
Rashid Jan Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia Author https://orcid.org/0000-0001-9709-7045
Fawad Hussain Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan Author https://orcid.org/0000-0001-9122-6029
Imran Qureshi College of Computer and Information Sciences, Imam Mohammed Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia Author https://orcid.org/0000-0002-5569-6127

DOI:

https://doi.org/10.31181/sor202778

Keywords:

CPyF values, Aggregation operators, Aczel-Alsina, Decision Making, MCDM

Abstract

Aggregation operators serve as fundamental mathematical tools for synthesizing multiple inputs into a single representative output. In this study, we introduce a family of aggregation operators (AOs) tailored to the framework of complex Pythagorean fuzzy sets (CPyFSs). Owing to their superior ability to capture both amplitude and phase information, CPyFSs offer enhanced flexibility in modeling uncertainty and vagueness, making them highly suitable for real-world decision-making problems. Motivated by these advantages, this paper develops several novel AOs within the CPyFS environment to address multi-attribute decision-making (MADM) problems more effectively. To further enhance the flexibility and robustness of the proposed operators, Aczél–Alsina (AA) operational laws are incorporated. In particular, we propose the complex Pythagorean fuzzy Aczél–Alsina Heronian mean (CPyFAAHM) operator and the complex Pythagorean fuzzy Aczél–Alsina geometric Heronian mean (CPyFAAGHM) operator, which integrate AA operations with Heronian mean and geometric Heronian mean structures. We investigate the key mathematical properties of the proposed operators, including their structural characteristics and aggregation behavior. Additionally, weighted versions of these operators are developed to accommodate the varying importance of decision attributes. Based on these operators, a MADM methodology is constructed for decision-making under the CPyFS framework. Finally, the effectiveness and practicality of the proposed approach are demonstrated through a numerical example, followed by a comparative analysis with existing MADM methods under complex Pythagorean fuzzy information, highlighting its superiority and applicability.

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