This study addresses the inherent uncertainty in human decision-making by leveraging fuzzy sets, which were introduced to better capture the imprecision associated with human thoughts and judgments. As an extension to traditional fuzzy sets, the Linear Diophantine Fuzzy Set (LDFS) was developed, offering a more flexible approach by relaxing existing limitations on grade values. The LDFS has found applications across various fields, demonstrating its versatility and effectiveness. In this study, we explore the application of the Linear Diophantine Fuzzy Set within the framework of the Combinative Distance-based Assessment (CODAS) method. The CODAS method stands out because it incorporates Euclidean and Taxicab distances. Decision-making should consider not only the direct distances between ideal solutions and alternatives but also the indirect distances. The foremost objective of this research is to propose a novel approach by integrating the CODAS method with the LDFS to address complex decision-making problems characterized by uncertainty and imprecision. To illustrate the practical utility of the proposed method, we apply it to a numerical example involving the selection of a logistics specialist, a critical decision in emergency logistics optimization. The research also includes a case study on a logistics specialist, highlighting the practical application of the methods discussed. Furthermore, this study provides a comprehensive sensitivity analysis of the parameters' weights to evaluate the robustness and reliability of the proposed method. The results highlight the effectiveness of the LDF CODAS method in making informed and reliable decisions under conditions of uncertainty, paving the way for future applications in other decision-making scenarios.

In the realm of cybersecurity, the formulation of comprehensive strategies is imperative for multinational corporations to protect against pervasive cyber threats. Recent developments in the field of intuitionistic multi-fuzzy sets (IMFSs) have heralded q-rung orthopair multi-fuzzy sets (MFSs) as a pivotal tool for encapsulating ambiguity and uncertainty within complex scenarios. The essence of this study lies in the introduction of two innovative distance measures tailored for q-rung orthopair MFSs (q-ROM$^{k}$FSs) of dimension k, enhancing the capacity to delineate distinctions between such sets effectively. Employing score functions pertinent to q-ROM$^{k}$FSs, this research extends its application to the sphere of Multi-Attribute Decision Making (MADM), presenting a methodological advancement in decision-making processes. The efficacy of the proposed measures is elucidated through a comparative analysis with existing methodologies in MADM, thereby underscoring the superiority of the introduced approach. This investigation not only contributes to the enrichment of the theoretical underpinnings of q-ROMFSs but also propels their practical application in cybersecurity strategy formulation for multinational entities. The study employs the Euclidean and Hamming distance measures as benchmarks, supplemented by the development of a score and accuracy function, to furnish a comprehensive tool for addressing cybersecurity challenges.

Location selection is a critical process in decision-making for projects that involve multiple criteria, such as urban planning, industrial site development, or green building projects. Multiple criteria decision making (MCDM) is a systematic approach that evaluates and ranks potential alternatives based on a set of often conflicting criteria. This study focuses on selecting the optimal urban location for a green building project by employing the \(L_{q}*\) q-rung orthopair multi-fuzzy soft-MCDM(\(L_{q}*\) q-ROMFS) techniques. The \(L_{q}*\) q-ROMFS set combines elements from two distinct theories with lattice ordering parameters: q-rung orthopair fuzzy set and multi-fuzzy soft set. It provides a mathematical framework with multiple parameters that effectively represents problems involving multi-dimensional data within a dataset. We expand this concept by establishing the algebraic structures of \(L_{q}*\) q-ROMFS sets, including properties like modularity and distributivity, while also analyzing their homomorphism under lattice mappings. Finally, leveraging the \(L_{q}*\) q-ROMFS matrix, we propose both a choice matrix and a weighted choice matrix to effectively address the selection of the optimal urban location for a green building project.

The need to grow in a secure and tranquil environment demands the efforts of an armed force, and only with a strong-armed force can a country ensure its national security. In military activities, communication devices are widely used to confuse enemies’ radars or communications to abandon their strategies and execute planned actions. The range of communication devices depends mainly on the antennas used. Army sustainability goals are to upgrade the effectiveness of the mission, reduce army environmental impact, build green sustainable structures, and attain the energy level independence that improves the continuity of operations which are indispensable to the mission. The primary goal of this paper is to present an innovative mathematical model for selecting pertinent antennae in communication devices using an innovative idea called a Complex Linear Diophantine Fuzzy Soft set based on the various attributes by incorporating decision-making techniques. Also, some of its beneficial operations such as Complement, AND, OR, Extended Union, and Extended Intersection, are presented in concert with the properties and theorems to apprise the viability of the proposed paper. This concept is more applicable and necessary to assess real-life situations using mathematical modeling.