In the realm of decision-making under uncertainty, Math Assignment Helper interval-valued Fermatean hesitant fuzzy sets (IVFHFSs) have emerged as a powerful tool. These sets address the complexities inherent in uncertain data, offering a nuanced approach to handling information that traditional methods may overlook. However, current multi-attribute group decision-making (MAGDM) techniques utilizing IVFHFSs face certain limitations that hinder their effectiveness.

Existing MAGDM methods based on IVFHFSs often lack a thorough exploration of operational laws and fail to adequately consider interattribute relationships, which are crucial in decision contexts involving multiple criteria. Moreover, their flexibility is constrained, limiting their applicability across diverse scenarios.

To overcome these challenges, this paper proposes a novel approach leveraging Einstein Bonferroni operators within the framework of IVFHFSs. The use of Einstein Bonferroni operators addresses the gaps in current methodologies by introducing enhanced operational laws tailored for uncertain data scenarios. These operators include the interval-valued Fermatean hesitant fuzzy Einstein Bonferroni mean and the interval-valued Fermatean hesitant fuzzy Einstein weighted Bonferroni mean under Einstein t-norms. By integrating these operators, the method considers attribute relationships more comprehensively and offers increased flexibility in decision-making processes.

Einstein Bonferroni Operators and Their Application

The foundation of this approach lies in the thorough examination of Einstein t-norms' operational laws under IVFHFSs. This exploration extends the theoretical underpinnings of IVFHFSs, paving the way for more robust decision models. The interval-valued Fermatean hesitant fuzzy Einstein Bonferroni mean operator and its weighted variant are specifically designed to aggregate uncertain data while respecting the intrinsic connections between attributes. Unlike traditional methods, which may treat attributes in isolation, these operators enable a holistic assessment that mirrors real-world decision dynamics more accurately.

Novel MAGDM Methodology

Building upon the theoretical developments of Einstein Bonferroni operators, this paper introduces a novel MAGDM method tailored to leverage these advancements effectively. This methodology integrates the newly developed operators within a structured decision-making framework, ensuring practical applicability across various domains. The proposed method not only enhances decision accuracy but also promotes transparency in decision processes by explicitly addressing attribute interdependencies.

Application and Validation

To validate the efficacy of the proposed method, a case study in cardiovascular disease diagnosis is presented. This application demonstrates how the introduced MAGDM approach can be applied in a critical healthcare context, where decisions must consider multiple factors with varying degrees of uncertainty. By utilizing the interval-valued Fermatean hesitant fuzzy Einstein Bonferroni operators, healthcare practitioners can make informed decisions that account for nuanced relationships between diagnostic criteria, ultimately leading to improved patient outcomes.

Conclusion

In conclusion, the integration of Einstein Bonferroni operators within the framework of interval-valued Fermatean hesitant fuzzy sets represents a significant advancement in multi-attribute group decision-making under uncertainty. By addressing the limitations of existing methods through enhanced operational laws and improved flexibility, this approach offers a more comprehensive toolset for decision-makers across industries. The cardiovascular disease diagnosis application underscores the practical utility of the proposed methodology, highlighting its potential to streamline complex decision processes and enhance decision quality. As research in this field progresses, further refinements and applications of these operators are expected to broaden their impact, paving the way for more robust and effective decision support systems in diverse domains.