The intuitionistic hesitant fuzzy set (IHFS) is an enriched version of hesitant fuzzy sets (HFSs) that can cover both fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). By assigning membership and non-membership grades as subsets of [0, 1], the IHFS can model and handle situations more proficiently. Another related theory is the theory of set pair analysis (SPA), which considers both certainties and uncertainties as a cohesive system and represents them from three aspects: identity, discrepancy, and contrary. In this article, we explore the suitability of combining the IHFS and SPA theories in multi-attribute decision making (MADM) and present the hybrid model named intuitionistic hesitant fuzzy connection number set (IHCS). To facilitate the design of a novel MADM algorithm, we first develop several averaging and geometric aggregation operators on IHCS. Finally, we highlight the benefits of our proposed work, including a comparative examination of the recommended models with a few current models to demonstrate the practicality of an ideal decision in practice. Additionally, we provide a graphical interpretation of the devised attempt to exhibit the consistency and efficiency of our approach.

For choosing the optimal option for multiple issues, the multiattribute decision-making (MADM) technique within a Fermatean fuzzy environment is a well-known and significant method. This paper presents a novel superiority inferiority ranking (SIR) approach for Fermatean fuzzy sets in group decision-making using multicriteria to reduce investment risk. This approach aims to evaluate the strategies for selecting the optimal investment company. The SIR method is depicted, and its effectiveness in decision-making is explored. In this manuscript, we develop new types of A$\mathcal{c}\mathcal{z}\mathcal{e}\mathcal{l}$–A$\mathcal{l}\mathcal{s}\mathcal{i}\mathcal{n}\mathcal{a}$ operations on the Fermatean fuzzy environment and Fermatean Fuzzy A$\mathcal{c}\mathcal{z}\mathcal{e}\mathcal{l}$–A$\mathcal{l}\mathcal{s}\mathcal{i}\mathcal{n}\mathcal{a}$ (FF-AA) average aggregation operators, including their properties such as idempotency, monotonicity, and boundedness. Further, we introduce a Fermatean fuzzy A$\mathcal{c}\mathcal{z}\mathcal{e}\mathcal{l}$–A$\mathcal{l}\mathcal{s}\mathcal{i}\mathcal{n}\mathcal{a}$ weighted average closeness coefficient (FF-AA-WA-$\mathcal{C}\mathcal{C}$) aggregation operator (AO) based on the closeness coefficient for MAGDM issues. By utilizing the proposed technique, we solve a numerical example of an MAGDM problem. The results show that this approach is accurate and practical, and consistent with a realistic investment circumstance. A demonstration was created to emphasize the significance and credibility of this approach and assess its validity by comparing its outcomes with the established methods.

Foreign Object Debris (FOD) presents a critical threat to aviation safety, with the potential to damage aircraft and jeopardize lives. This study explores the use of Deep Convolutional Neural Networks (DCNNs) for the precise detection and classification of FOD, aiming to transform existing prevention strategies. By employing models such as Xception and YOLOv8, the system achieved detection accuracies of up to 98% on diverse datasets. The integration of AI-based approaches significantly enhances operational efficiency, contributing directly to the United Nations Sustainable Development Goals (SDGs), particularly SDG 9: Industry, Innovation, and Infrastructure: Industry, Innovation, and Infrastructure, by promoting smart, safe, and sustainable aviation systems. The findings highlight the pivotal role of innovation in strengthening critical transportation infrastructure and ensuring resilient airport operations aligned with global development goals.

Intuitionistic fuzzy information is a potent tool for medical diagnosis applications as it can represent imprecise and uncertain data. However, making decisions based on this information can be challenging due to its inherent ambiguity. To overcome this, power aggregation operators can effectively combine various sources of information, including expert opinions and patient data, to arrive at a more accurate diagnosis. The timely and accurate diagnosis of medical conditions is crucial for determining the appropriate treatment plans and improving patient outcomes. In this paper, we developed a novel approach for the three-way decision model by utilizing decision-theoretic rough sets and power aggregation operators. The decision-theoretic rough set approach is essential in medical diagnosis as it can manage vague and uncertain data. The redesign of the model using interval-valued classes for intuitionistic fuzzy information further improved the accuracy of the diagnoses. The intuitionistic fuzzy power weighted average (IFPWA) and intuitionistic fuzzy power weighted geometric (IFPWG) aggregation operators are used to aggregate the attribute values of the information system. The established operators are used to combine information within the intuitionistic fuzzy information system. The outcomes of various alternatives are then transformed into interval-valued classes through discretization. Bayesian decision rules, incorporating expected loss factors, are subsequently generated based on this foundation. This approach helps in effectively combining various sources of information to arrive at more accurate diagnoses. The proposed approach is validated through a medical case study where the participants are classified into three different regions based on their symptoms. In conclusion, the decision-theoretic rough set approach, along with power aggregation operators, can effectively manage vague and uncertain information in medical diagnosis applications. The proposed approach can lead to timely and accurate diagnoses, thereby improving patient outcomes.

In this study, a novel Pythagorean fuzzy aggregation operator is presented by combining the concepts of Aczel–Alsina () T-norm and T-conorm operations for multiple attribute group decision-making (MAGDM) challenge for the superiority and inferiority ranking (SIR) approach. This approach has many advantages in solving real-life problems. In this study, the superiority and inferiority ranking method is illustrated and showed the effectiveness for decision makers by using multicriteria. The Aczel–Alsina aggregation operators on interval-valued IFSs, hesitant fuzzy sets (HFSs), Pythagorean fuzzy sets (PFSs), and T-spherical fuzzy sets (TSFSs) for multiple attribute decision-making (MADM) issues have been proposed in the literature. In addition, we propose a Pythagorean fuzzy Aczel–Alsina weighted average closeness coefficient () aggregation operator on the basis of the closeness coefficient for MAGDM challenges. To highlight the relevancy and authenticity of this approach and measure its validity, we conducted a comparative analysis with the method already in vogue.

Q-rung orthopair fuzzy sets have been proven to be highly effective at handling uncertain data and have gained importance in decision-making processes. Torra’s hesitant fuzzy model, on the other hand, offers a more generalized approach to fuzzy sets. Both of these frameworks have demonstrated their efficiency in decision algorithms, with numerous scholars contributing established theories to this research domain. In this paper, recognizing the significance of these frameworks, we amalgamated their principles to create a novel model known as Q-rung orthopair hesitant fuzzy sets. Additionally, we undertook an exploration of Aczel–Alsina aggregation operators within this innovative context. This exploration resulted in the development of a series of aggregation operators, including Q-rung orthopair hesitant fuzzy Aczel–Alsina weighted average, Q-rung orthopair hesitant fuzzy Aczel–Alsina ordered weighted average, and Q-rung orthopair hesitant fuzzy Aczel–Alsina hybrid weighted average operators. Our research also involved a detailed analysis of the effects of two crucial parameters: $\lambda$, associated with Aczel–Alsina aggregation operators, and N, related to Q-rung orthopair hesitant fuzzy sets. These parameter variations were shown to have a profound impact on the ranking of alternatives, as visually depicted in the paper. Furthermore, we delved into the realm of Wireless Sensor Networks (WSN), a prominent and emerging network technology. Our paper comprehensively explored how our proposed model could be applied in the context of WSNs, particularly in the context of selecting the optimal gateway node, which holds significant importance for companies operating in this domain. In conclusion, we wrapped up the paper with the authors’ suggestions and a comprehensive summary of our findings.