A q-rung orthopair spherical fuzzy rough graph approach for modeling uncertain agricultural networks

In this paper, we propose a novel hybrid structure termed the q-rung orthopair spherical fuzzy rough graphs (q-ROSFRG) by integrating q-rung orthopair spherical fuzzy sets, rough set theory, and graph theory within rough approximation spaces. The proposed model generalizes classical fuzzy graphs and spherical fuzzy graphs by incorporating q-rung orthopair spherical fuzzy information, which effectively captures positive, neutral, and non-membership degrees under the flexible constraint $[\varsigma {]}^q+[\varrho {]}^q+[\varkappa {]}^q\le 1$, where $q\ge 1$ is a tunable parameter. We study the basic features of our proposed structure, such as the idempotency of approximation operators, duality by the complement, and connectivity related-inclusions. Furthermore, a group decision-making framework based on the q-ROSFRG model is developed to address uncertain path selection problems in network-based environments. The proposed algorithm handles vagueness and uncertainty in network data through lower and upper approximations combined with a maximin path strength criterion, proceeding iteratively from the source to target nodes. The practicality and efficiency of the suggested method are verified via a real application on agricultural irrigation network selection. In contrast to the existing fuzzy rough models that are designed to pick the best option from a finite set, the q-ROSFRG model tackles a fundamentally different problem: Finding the best connected path in a network while preserving its topological nature.