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.

This manuscript presents a novel All-pair shortest path algorithm that enhances Floyd’s method by integrating a soft computing-based decision model tailored for transportation routing in an uncertain environment. The routing problem is formulated as a graph, where the edges are aggregated into a single representative weight from multiple influencing factors using an aggregation operator and the score function. These weights represent pollution levels based on air quality data collected by the AirQo monitoring device along different route segments. By integrating decision making method, the enhanced Floyd’s algorithm is then used to compute the most effective route between a defined source and destination. The proposed method supports healthier travel choices by identifying routes with comparatively cleaner air. Preliminary simulations indicate that the suggested technique facilitates more informed route selection compared to conventional approaches. The uniqueness of this method lies in its integration of classical graph theory with decision-making for real-time environmental sensing, offering reduced exposure to pollutants and supporting cleaner, safer mobility in urban environments.