An α-Cut Optimization Framework for Modular EV Charging Station Design Under Fuzzy Uncertainty

This paper develops a unified α-cut optimization framework for modular electric vehicle (EV) fast-charging station design under fuzzy uncertainty. Uncertain peak demand, annual delivered energy, electricity price, ambient temperature, arrival rate, and energy per session are represented by triangular or trapezoidal fuzzy numbers and reformulated through α-cut bounds. The resulting design problem is expressed as a hybrid discrete–continuous model in which the number of modules, the selected catalog module rating, installed power, cooling provision, and a station-volume proxy are jointly optimized. An aggregated representation of interchangeable modules is adopted to remove permutation-equivalent descriptions and preserve a compact search space. Three planning views are examined: minimum CAPEX at a prescribed α-cut level, minimum loss-driven OPEX under a CAPEX budget, and a service-oriented admissibility/coverage analysis that avoids interpreting larger α values as greater robustness. The strengthened numerical study includes a deterministic nominal benchmark, peak demand sensitivity regimes, feasibility threshold and budget sweep results, explicit service stress scenarios, and a queueing sensitivity check against Erlang-C and discrete-event simulation indicators. The results show that baseline CAPEX designs may be dominated by catalog thresholds, whereas OPEX and service-oriented conclusions become informative once budget and traffic regimes are varied. The proposed framework is therefore positioned as a tractable α-cut-based design screening and comparative optimization tool for representative modular EV charging station scenarios, rather than as a universally validated operational design rule.