Optimizing decision making with Fermatean fuzzy soft Hamachar operators in the analysis of anaphylaxis (a
Aurang Zeb1, Nasir Ali2, Muhammad Riaz3
1Business School of Xi'an International University, Xi'an, 710077, Shaanxi, China.
Insights
Fermatean fuzzy soft sets (FFSS) model complex, uncertain data from childhood food allergies and anaphylaxis. Novel Hamacher operators enhance decision-making for identifying at-risk patients, improving emergency response and care.
Area of Science:
- Fuzzy set theory
- Decision analysis
- Computational intelligence
Background:
- Childhood food allergies pose life-threatening risks, particularly anaphylaxis.
- Anaphylaxis is a complex condition with uncertain symptoms requiring precise medical management.
- Existing decision-making models struggle with multi-faced and uncertain data inherent in anaphylaxis cases.
Purpose of the Study:
- Introduce the Fermatean fuzzy soft set (FFSS) to model complex, uncertain information.
- Develop novel Fermatean fuzzy soft Hamacher weighted averaging and geometric operators.
- Establish an approach for multiple attribute decision-making (MADM) problems using FFSS.
Main Methods:
- Utilized the Hamacher class of parametric norms for operator development.
- Applied FFSS and the developed operators to a decision-making problem.
- Examined operator performance by varying the constant ∂ for information aggregation.
- Investigated the generalization capabilities of triangular norms and the flexibility of Hamacher norms.
Main Results:
- The FFSS approach effectively models multi-faced and uncertain data.
- Novel Hamacher operators demonstrated enhanced differentiation between membership grades with varying ∂.
- The study confirmed the flexibility and broader uncertainty modeling scope of Fermatean fuzzy sets and Hamacher norms.
- Parameterization via soft set theory offers tailored uncertainty representation for complex scenarios.
Conclusions:
- FFSS provides a robust framework for decision-making in complex medical scenarios like anaphylaxis.
- The developed Hamacher operators offer improved data fusion and decision support.
- The findings highlight the potential of FFSS and generalized norms for advanced uncertainty modeling and future research in fuzzy extensions.
Abstract:
The accessibility of affordable medication and emergency response care is essential in preserving the health of children. More youngsters are discovered to suffer from food allergies and are at risk of having life-threatening Anaphylactic responses. Without prompt medical attention, Anaphylaxis can be fatal. The condition is complex as it depends on several factors and exhibits uncertainties due to a range of symptoms. To model multi-faced and uncertain information in these cases, we introduce a fuzzy soft notion, known as the Fermatean fuzzy soft set (FFSS). To fuse this multi-faced data, the Hamacher class of parametric norms are utilized to define novel Fermatean fuzzy soft Hamacher weighted averaging and geometric operators. Data modelling via FFSS, and developed operators are utilized to establish an approach for solving multiple attribute decision making problems. Finally, a decision making (DM) problem related to identifying patients based on symptoms of Anaphylaxis (an allergic reaction that is severe and potentially devastating) is provided for verifying the approach and its practical demonstration. The performance of the operators is examined by aggregating information through different values of the constant ∂. The results revealed that aggregated scores rose significantly for varying ∂, reflecting an enhanced differentiation between membership grades. The insights into the impact of ∂ are crucial for selecting the appropriate value in FFSNs, enabling the representation of uncertainty and preferences tailored to various complex DM scenarios. Additionally, it is observed that the triangular norms investigated by classical logic for fuzzy logic are generalizations of the typical two-valued logical conjunction and serve to build the foundation for aggregation operators. The Hamacher norms, being the generalization of algebraic norms, are more flexible. Also, the spatial scope of the Fermatean fuzzy set (FFS) is larger, offering a larger space for uncertainty modelling. The parameterization tool is provided by the addition of soft set theory. These observations are vital for further research, offering a wide range of possibilities to build on in terms of defining operators and novel fuzzy extensions.
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