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    This study introduces new intuitionistic fuzzy aggregation operators, the intuitionistic fuzzy Archimedean Heronian aggregation (IFAHA) and intuitionistic fuzzy weight Archimedean Heronian aggregation (IFWAHA) operators, for improved decision-making.

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    Area of Science:

    • Fuzzy Set Theory
    • Decision Sciences
    • Aggregation Operators

    Background:

    • Archimedean t-conorm and t-norm offer general operational rules for intuitionistic fuzzy numbers (IFNs).
    • Existing aggregation operators can be generalized using these rules.
    • The Heronian mean (HM) effectively captures interrelationships between attributes.

    Purpose of the Study:

    • To extend the Heronian mean (HM) to intuitionistic fuzzy numbers (IFNs).
    • To develop intuitionistic fuzzy HM operators utilizing Archimedean t-conorm and t-norm.
    • To introduce a novel multiple attribute group decision making (MAGDM) method.

    Main Methods:

    • Discussing intuitionistic fuzzy operational rules based on Archimedean t-conorm and t-norm.
    • Proposing the intuitionistic fuzzy Archimedean Heronian aggregation (IFAHA) operator.
    • Proposing the intuitionistic fuzzy weight Archimedean Heronian aggregation (IFWAHA) operator.
    • Developing a new MAGDM method leveraging the proposed operators.

    Main Results:

    • Introduction of the IFAHA and IFWAHA operators.
    • Analysis of the properties and special cases of the new operators.
    • Demonstration of a MAGDM method using the proposed operators.

    Conclusions:

    • The developed IFAHA and IFWAHA operators provide effective tools for handling intuitionistic fuzzy information.
    • The proposed MAGDM method, based on these operators, is effective for complex decision-making scenarios.
    • This research enhances aggregation techniques within fuzzy set theory for practical applications.