Complex fermatean fuzzy N-soft sets: a new hybrid model with applications

Area of Science:

• Decision Sciences
• Fuzzy Set Theory
• Multi-Attribute Decision Making

Background:

• Human decision-making involves complex choices with satisfaction and dissatisfaction elements.
• Existing methods may not fully capture this dual nature of preferences.
• Fuzzy set theory offers frameworks for uncertainty, but extensions are needed.

Purpose of the Study:

• To introduce complex Fermatean fuzzy N-soft sets (S) for decision-making.
• To develop and validate an S-TOPSIS approach for multi-attribute decision making.
• To enhance the handling of two-dimensional information in decision models.

Main Methods:

• Definition of fundamental set-theoretic operations for S.
• Development of algebraic and Yager operations for S numbers.
• Implementation of S-based algorithms and an S-TOPSIS approach with novel operators.

Main Results:

• The proposed S model effectively handles dual-dimensional decision information.
• The S-TOPSIS approach demonstrated superior performance in classification and selection tasks.
• Comparative analyses confirmed the validity, feasibility, and reliability of the S and S-TOPSIS models.

Conclusions:

• Complex Fermatean fuzzy N-soft sets provide a robust framework for decision-making.
• The developed S-TOPSIS method offers advantages over existing techniques.
• The approach is applicable to real-world problems, such as selecting optimal locations.