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Complex Fermatean fuzzy extended TOPSIS method and its applications in decision making
Muhammad Zaman1, Fazal Ghani1, Asghar Khan1
1Department of Mathematics, Abdul Wali Khan University, Mardan, KP, Pakistan.
Heliyon
|October 9, 2023
Summary
This study introduces new decision-making techniques using complex Fermatean fuzzy numbers and Einstein t-norms. These methods enhance handling uncertainty and ambiguity in complex problems, demonstrated through an instructor selection example.
Area of Science:
- Mathematics
- Computer Science
- Decision Sciences
Background:
- Traditional fuzzy sets have limitations in representing negative aspects.
- Fermatean fuzzy sets address these limitations by incorporating negative aspects.
- Complex Fermatean fuzzy sets offer enhanced capabilities for managing ambiguity and uncertainty.
Purpose of the Study:
- To develop novel decision-making techniques utilizing complex Fermatean fuzzy numbers.
- To introduce new aggregation operators based on Einstein t-norms for complex Fermatean fuzzy numbers.
- To apply these techniques to complex multi-attribute group decision-making (MAGDM) problems.
Main Methods:
- Construction of complex Fermatean fuzzy Einstein weighted average (CFFEWAA), ordered weighted average (CFFEOWAA), and hybrid average (CFFEHAA) aggregation operators.
- Analysis of the fundamental properties of the proposed aggregation operators.
- Development of algorithms and an extended TOPSIS method for decision-making based on these operators.
Main Results:
- Successfully defined and analyzed novel aggregation operators for complex Fermatean fuzzy numbers.
- Demonstrated the application of these operators and the extended TOPSIS method to a practical MAGDM problem (English instructor selection).
- Validated the effectiveness of the proposed models through comparison with existing methods.
Conclusions:
- The proposed complex Fermatean fuzzy aggregation operators and extended TOPSIS method provide effective tools for complex decision-making under uncertainty.
- The developed techniques offer a robust framework for addressing ambiguity in multi-attribute group decision-making scenarios.
- This research contributes to the advancement of fuzzy set theory and its applications in practical decision support systems.
Keywords:
Complex Fermatean fuzzy Einstein hybrid average (CFFEHA) operatorComplex Fermatean fuzzy set (CFFS)Einstein aggregation operatorsMulti-attribute group decision-making (MAGDM)TOPSIS methodMore Related Videos
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