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Multi-attribute decision-making methods based on Aczel–Alsina power aggregation operators for managing complex intuitionistic fuzzy sets

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Abstract

Aczel–Alsina t-norm and t-conorm were derived by Aczel and Alsina in 1982, which were the modified or extended forms of algebraic t-norm and t-conorm. Furthermore, the power aggregation operator is also a very significant and precious method that is used for evaluating the finest preference from the collection of finite preferences. Inspired by the above theories, we concentrate to derive the theory of Aczel–Alsina power aggregation operators for C-IF information, such as C-IFAAPA, C-IFAAWPA, C-IFAAPG, and C-IFAAWPG operators. Moreover, we derive the theory of idempotency and prove that the property of monotonicity and boundedness failed with the help of some counterexamples. Additionally, we evaluate a MADM approach to derive operators in the presence of C-IF information. Finally, we illustrative practical examples for comparing the derived work with various existing or prevailing operators to show the supremacy and proficiency of the derived information.

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Abbreviations

C-IF:

Complex intuitionistic fuzzy

MG:

Membership grade

NMG:

Non-membership grade

C-IFAAPA:

Complex intuitionistic fuzzy Aczel–Alsina power averaging

C-IFAAWPA:

Complex intuitionistic fuzzy Aczel–Alsina weighted power averaging

C-IFAAPG:

Complex intuitionistic fuzzy Aczel–Alsina power geometric

C-IFAAWPG:

Complex intuitionistic fuzzy Aczel–Alsina weighted power geometric

MADM:

Multi-attribute decision-making

FS:

Fuzzy set

IFS:

Intuitionistic fuzzy set

C-FS:

Complex fuzzy set

C-IFS:

Complex intuitionistic fuzzy set

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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. Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, 44000, Pakistan

    Tahir Mahmood & Zeeshan Ali

  2. KERMIT, Department of Mathematical Modeling, Statistics and Bioinformatics, Coupure links 653, Ghent University, Ghent, Belgium

    Zeeshan Ali

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  1. Tahir Mahmood
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  2. Zeeshan Ali
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Mahmood, T., Ali, Z. Multi-attribute decision-making methods based on Aczel–Alsina power aggregation operators for managing complex intuitionistic fuzzy sets. Comp. Appl. Math. 42, 87 (2023). https://doi.org/10.1007/s40314-023-02204-1

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  • DOI: https://doi.org/10.1007/s40314-023-02204-1

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