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Complex Pythagorean Hesitant Fuzzy Aggregation Operators Based on Aczel-Alsina t-Norm and t-Conorm and Their Applications in Decision-Making

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Abstract

Aggregation operators are used for aggregating the collection of finite information into a singleton set. The Aczel-Alsina t-norm and t-conorm are very useful for constructing any kind of new aggregation operators, which was presented by Aczel and Alsina in 1982. Moreover, complex Pythagorean fuzzy (CPF) sets and hesitant fuzzy (HF) sets are the most generalized and very useful techniques to cope with unreliable and awkward information in genuine life problems. In this manuscript, we combine the HF set and CPF set to derive the complex Pythagorean hesitant fuzzy (CPHF) set and its fundamental laws. Furthermore, we evaluate the Aczel-Alsina operational laws based on Aczel-Alsina norms and CPHF information. Additionally, based on the Aczel-Alsina operational laws for CPHF information, we investigate the CPHF Aczel-Alsina-weighted averaging (CPHFAAWA) operator, CPHF Aczel-Alsina-ordered weighted averaging (CPHFAAOWA) operator, CPHF Aczel-Alsina-weighted geometric (CPHFAAWG) operator, and CPHF Aczel-Alsina-ordered weighted geometric (CPHFAAOWG) operator. Some remarkable properties are also examined for the invented theory. Moreover, a multi-attribute decision-making (MADM) technique is presented based on discovered operators for CPHF information. Finally, we aim to illustrate some examples for comparing the proposed techniques with some existing ones to show the worth and feasibility of the discovered approaches.

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Acknowledgements

The authors acknowledge with thanks to reviewers for taking the time and effort necessary to review the manuscript. The authors sincerely appreciate all valuable comments and suggestions which contributed to improving the quality of the manuscript.

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Authors and Affiliations

  1. School of International Business, Qingdao Huanghai University, Qingdao, 266427, Shandong, China

    Zaifu Sun & Peide Liu

  2. Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan

    Zeeshan Ali

  3. Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan

    Zeeshan Ali & Tahir Mahmood

  4. Shandong Key Laboratory of New Smart Media, Jinan, 250014, Shandong, China

    Peide Liu

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  1. Zaifu Sun
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  2. Zeeshan Ali
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  3. Tahir Mahmood
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  4. Peide Liu
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All authors contributed equally.

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Correspondence to Peide Liu.

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Sun, Z., Ali, Z., Mahmood, T. et al. Complex Pythagorean Hesitant Fuzzy Aggregation Operators Based on Aczel-Alsina t-Norm and t-Conorm and Their Applications in Decision-Making. Int. J. Fuzzy Syst. (2024). https://doi.org/10.1007/s40815-023-01613-y

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  • DOI: https://doi.org/10.1007/s40815-023-01613-y

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