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Aczel Alsina t-norm and t-conorm-based aggregation operators under linguistic interval-valued intuitionistic fuzzy
Afra Siab1, Muhammad Sajjad Ali Khan2, Muhammad Asif Jan1
1Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, Pakistan.
Peerj. Computer Science
|June 10, 2024
Summary
This study introduces new Aczel-Alsina aggregation operators for linguistic interval-valued intuitionistic fuzzy sets. These operators enhance multi-criteria group decision-making (MCGDM) with improved applicability and validity in real-world scenarios.
Area of Science:
- Fuzzy Set Theory
- Decision Sciences
- Computational Intelligence
Background:
- Interval-valued intuitionistic fuzzy sets (IVIFSs) offer enhanced representation for uncertainty.
- Aggregation operators are crucial for consolidating information in decision-making.
- Existing operators may not fully capture the nuances of linguistic and interval-valued fuzzy information.
Purpose of the Study:
- To develop novel aggregation operators based on the Aczel-Alsina t-norm and t-conorm for linguistic interval-valued intuitionistic fuzzy numbers.
- To establish rules for the operational behavior of these numbers.
- To propose a multi-criteria group decision-making (MCGDM) method utilizing the new operators.
Main Methods:
- Definition of operational rules for linguistic interval-valued intuitionistic fuzzy numbers.
- Construction of several Aczel-Alsina-based aggregation operators (e.g., LIVIFAAWA, LIVIFAAWG, LIVIFAAOWA, LIVIFAAOWG, LIVIFAAHWA, LIVIFAAHWG).
- Theoretical analysis of the properties of the developed operators.
- Application of the operators within an MCGDM framework.
Main Results:
- Successful creation of a suite of linguistic interval-valued intuitionistic fuzzy Aczel-Alsina aggregation operators.
- Demonstration of desirable properties inherent in the new operators.
- Validation of the proposed MCGDM method through application to practical decision-making problems.
Conclusions:
- The developed Aczel-Alsina aggregation operators effectively handle linguistic interval-valued intuitionistic fuzzy information.
- The proposed MCGDM method provides a robust and applicable approach for complex decision problems.
- The new operators and method show superior performance compared to existing techniques.
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