<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\partial\)</EquationSource> </InlineEquation>. The results revealed that aggregated scores rose significantly for varying <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\partial\)</EquationSource> </InlineEquation>, reflecting an enhanced differentiation between membership grades. The insights into the impact of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\partial\)</EquationSource> </InlineEquation> 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.</p>

Optimizing decision making with Fermatean fuzzy soft Hamachar operators in the analysis of anaphylaxis (a life-threatening allergic reaction)

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2026年4月5日

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Aurang Zeb,
Nasir Ali,
Muhammad Riaz,
Hu Zhao,
Muhibullah Mahboob,
Muzhou Hou

摘要

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 \(\partial\) . The results revealed that aggregated scores rose significantly for varying \(\partial\) , reflecting an enhanced differentiation between membership grades. The insights into the impact of \(\partial\) 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.