The ecological transition and decarbonization agenda have brought energy poverty into sharp focus. However, despite growing policy and academic attention, consensus on its definition or measurement remains elusive. This paper proposes a novel multidimensional energy poverty index based on a fuzzy set approach (fMEPI), addressing three key principles: the multifactorial nature of energy poverty, the limitations of binary classifications, and the need for indicators computable at local scales. Drawing on administrative, census, and modelled data, the index integrates five dimensions: housing conditions and energy efficiency, residential energy consumption, financial capacity, climate conditions, and energy-related needs. Applied to the Lombardy region (Italy), results reveal that vulnerability is concentrated in mountainous and hilly areas, and that large municipalities exhibit significant intra-urban heterogeneity. The proposed methodology offers a practical tool for regional and local authorities to design and target policies against energy poverty.