Authors: Siddalingaswamy R, Yogeesh N, Rajathagiri D T, M. S. Sunitha, Jagadeesha K C
Abstract: This study develops a practical modeling pipeline to treat epistemic uncertainty in sustainability-focused partial differential equations governing environmental and urban systems. We represent imprecise forcings and parameters with fuzzy numbers (triangular/trapezoidal membership functions) and propagate uncertainty via α-level analysis: for each α, parameters are mapped to compact intervals and a deterministic diffusion–reaction problem is solved to yield envelopes of feasible states. The workflow integrates (i) fuzzy parameterization and α-cut computation, (ii) numerically stable parabolic solvers (implicit/Crank–Nicolson discretizations with Dirichlet boundaries), and (iii) a stylized robust multi-objective design that visualizes trade-offs between expected performance and sustainability risk. Two representative applications illustrate relevance: groundwater-style storage under uncertain recharge–demand balance and urban heat mitigation with uncertain material/forcing properties. Results include interpretable membership curves and α-cut bounds, α-dependent terminal profiles, time-evolution bands that communicate worst-plausible excursions, and Pareto fronts clarifying yield–risk compromise under policy intensity. A grid-refinement study indicates indicative second-order spatial convergence in the smooth-solution regime, supporting numerical consistency. Beyond these cases, the framework is modular and extensible to nonlinear physics, higher dimensions, and hybrid fuzzy–stochastic formulations, while remaining transparent for expert elicitation and decision support. Overall, the approach preserves uncertainty structure without imposing unwarranted probability models, providing decision-makers with conservative, policy-ready indicators for risk-aware planning in data-sparse contexts
DOI: http://doi.org/10.5281/zenodo.17617766
