The state of bipolarity plays a major role in any circumstance due to the involvement of fors and againsts for each condition. This research enhances some rudimentary operations, propositions, and valuable theorems based on the recently developed aspect called the bipolar linear diophantine fuzzy hypersoft set. The choice of the individual without restriction enhances the technique. In addition, all its crumbles are curtailed with more flexibility. Railways are easily accessible for all classes of people and require a guarded journey. Currently, rail accidents are a major controversy all over the world as they kill many and injure riskily. For this reason, an algorithm is expanded to elect an effective crash-evasive rail carriage equipped with ultrasonic sensors to detect the range of the hindrance and brake controls. The study aims to gain additional insight and solve the critical issue of railway safety, particularly regarding recent incidents that have placed passengers at risk worldwide. The initiative aims to develop a highly effective crash-evasive rail carriage system by extending the capabilities of existing algorithms. This technology aims to minimize the incidence of rail accidents by selecting an ideal system based on the sensing range of sensor and brake control mechanisms. The study further distinguishes its innovations to set theoretic operations within the framework plays a vital role in strengthening procedures for making choices and guaranteeing the accuracy of the proposed solution. The recommended strategy not only confronts current safety concerns but also sets the foundation for future technological evolution in the railway sector.

In response to the energy crisis and the global push for sustainability, modern power grids are increasingly integrating renewable energy, plug-in electric vehicles, and energy storage systems. This evolution demands an advanced energy management system capable of handling the variability of renewable resources, uncertainties in electric vehicle performance, fluctuating electricity prices, and dynamic load conditions. To address these challenges, our study introduces a novel decision-making framework that leverages a new score function for comparing q-rung orthopair multi-fuzzy soft numbers. This approach employs the Criteria Importance Through Inter-criteria Correlation (CRITIC) method to determine objective weights while simultaneously incorporating subjective preferences through an integrated weighting scheme. The framework is further enhanced by applying the Combined Compromise Solution (CoCoSo) method within the Lq* q-rung orthopair multi-fuzzy soft decision-making structure to select optimal energy management policies. Extensive sensitivity analysis confirms the robustness and effectiveness of the proposed methodology, offering a promising solution for efficient energy management in modern power systems.

This study offers a comprehensive analysis of novel information for linear diophantine multi-fuzzy sets and illustrates its applications in practical scenarios. We introduce innovative similarity metrics tailored for linear diophantine multi-fuzzy sets, including Cosine similarity, Jaccard similarity, and Exponential similarity. Additionally, we propose Entropy, Inclusion, and Distance measures, providing a robust theoretical foundation supported by developed theorems that explain the interactions between these metrics. The practical implications of these theoretical advancements are demonstrated through various case studies. Specifically, we apply the similarity measures to predict preeclampsia, a severe condition affecting pregnant women, showcasing their potential in medical diagnostics. The entropy measure is used to identify the optimal materials manufacturing method for medical surgical robots, underscoring its importance in ensuring patient safety and the effectiveness of medical procedures. Furthermore, the inclusion measure is employed in pattern recognition tasks, highlighting its utility in complex data analysis. The comparative and superiority analysis shows the effectiveness of our research. The novel aspect of this study is the implementation of information metrics for LDMFS. These efforts aim to enhance the impact and practical applicability of linear diophantine multi-fuzzy sets, fostering innovation and improving outcomes across multiple fields.

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.