Integrated evaluation of façade complexity in traditional Turkish and Greek houses: a fractal dimension and TOPSIS approach

This study quantitatively evaluates the façade-based geometric complexity of traditional Turkish and Greek houses in Safranbolu, Türkiye, by integrating fractal dimension (FD) analysis with the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The dataset comprised 16 houses (12 Turkish and four Greek), with the south, west, north, and east façades analyzed separately using the box-counting method. Façade-specific FD values were integrated using TOPSIS under an equal-weight baseline configuration. The results revealed considerable variation among individual buildings within both groups. The TOPSIS ranking was identical to that obtained from the arithmetic mean of the four façade FD values (Spearman’s ρ = 1.000), while sensitivity analysis under alternative weighting scenarios showed strong rank correlations with the baseline (ρ = 0.894–0.976). The Mann–Whitney U test identified no statistically significant difference between the two groups (U = 22.000, p = 0.862), with a very small effect size (|r| = 0.046). Given the small and unbalanced sample, this result should not be interpreted as evidence of equivalence between the two architectural traditions. The proposed framework provides a structured quantitative approach to façade complexity assessment, although its transferability requires validation on larger, more diverse datasets.