هندسۀ هوشمندی: خوانشی داده‌محور از شش بُعد تکوینی شهرهای هوشمند معاصر اروپایی

این پژوهش تلاشی برای بازتعریف منطق ارزیابی هوشمندی ‌شهری از منظر هندسۀ ‌هوشمندی در شهرهای ‌اروپایی است؛ قاره‌ای که تنوع تاریخی، نهادی و فناورانۀ آن بستری مناسب برای سنجش الگوهای تحول ‌شهری فراهم می‌کند. مطالعۀ حاضر با هدف تبیین چهارچوبی تحلیلی برای مقایسه و شناسایی الگوهای تکوینی شهرهای‌هوشمند در بسترهای متنوع اروپایی، مجموعه‌ای از شاخص‌ها را که ذیل شش‌ بُعد بنیادین شهر هوشمند (اقتصاد، مردم، حکمروایی، جابه‌جایی، محیط‌زیست و زندگی) تعریف شده‌اند، تدوین می‌کند. در این چهارچوب، هندسۀ ‌هوشمندی، به‌عنوان الگوی ساختاری توزیع و توازن ابعاد شش‌گانۀ شهر هوشمند در فضای چندبعدی تعریف می‌شود. موردهای مطالعه نیز براساس دسترس‌پذیری داده‌های رسمی پایگاه‌های معتبر اتحادیۀ ‌اروپا و پوشش شاخص‌های شش‌گانۀ شهر هوشمند انتخاب شده‌اند. برای سنجش شاخص‌ها، چهار روش تصمیم‌گیری‌ چندمعیاره شامل ahp، saw، topsis و vikor به ‌کار گرفته شده‌اند که هریک از منظری متفاوت به وزن‌دهی و رتبه‌بندی می‌پردازند. تفاوت رتبه‌ها با آزمون ناپارامتریک فریدمن ارزیابی شده و با تحلیل جبران‌پذیری، شاخص‌های مسلط و توافق روش‌ها، رتبه‌بندی نهایی و تیپ‌های هندسی ‌هوشمندی استخراج و مختصات شش‌بعدی هر شهر برای تبیین هندسۀ ‌هوشمندی ارائه شد. یافته‌ها نشان می‌دهند که هندسۀ ‌هوشمندی شهرهای اروپا الگوی واحدی ندارند، بلکه منظومه‌ای چند ریخت شامل چهار تیپ اصلی هستند: هستۀ متوازن شمال‌ اروپا، الگوی سخت‌افزارمحور غرب ‌اروپا، الگوی نرم‌افزارمحور انسانی، و هستۀ توافق منفی در جنوب و شرق. تحلیل‌ نهایی نشان می‌دهد که مسیر هوشمندی ‌اروپا به‌‌سوی واگرایی ساختاری و تفاوت‌های پایدار حرکت می‌کند. این مطالعه، با ارائۀ چهارچوبی تلفیقی برای سنجش چندوجهی شهرهای‌ هوشمند، برای تصمیم‌سازی داده‌محور در مدیریت‌شهری اروپایی مسیر تازه‌ای می‌گشاید و الگویی قابل ‌تعمیم برای سایر مناطق درحال‌ گذار به زیست‌بوم‌های شهری ‌هوشمند عرضه می‌کند.

the geometry of smartness: a data-driven interpretation of six dimensions shaping contemporary smart cities

introductionsmart cities have become a central paradigm in contemporary urban research, transforming how cities are measured, compared, and governed. yet despite the global diffusion of the concept, the internal structure of smartness remains uneven, multidimensional, and strongly dependent on local capacities for data production, governance, and innovation. europe, unlike many other regions of the world, benefits from a rich statistical ecosystem that enables cities to be evaluated across multiple dimensions using reliable, comparable, and annually updated indicators. this study builds upon these datasets to develop a six-dimensional analytical geometry of smartness across european cities. it aims to move beyond simple rankings and construct a deeper structural understanding of how cities behave across economic, people, governance, mobility, environmental, and living dimensions. the broader motivation of the research is twofold. first, it seeks to reveal the spatial and conceptual diversity of european smart cities, showing that smartness is not a uniform path but a set of distinct patterns and typologies. second, it aims to establish a theoretical–analytical device adaptable to other regions, including data-scarce contexts, where smart-city strategies remain fragmented due to the absence of structured statistical systems.theoretical frameworkthe study is grounded in the six-dimensional model widely adopted in the european smart-city literature (six dimensions), originally articulated by giffinger and subsequently refined by contemporary scholarship. this framework conceptualizes smartness as a balance between technological infrastructure (hard assets) and human–institutional capacity (soft assets). european parliament reports, urban audit methodology, and recent studies emphasize that the most successful smart cities cultivate harmony among these dimensions rather than privileging any single component. building on this foundation, the research introduces the concept of smartness geometry, which treats each city as a six-coordinate point in a multidimensional space. the geometric shape derived from these coordinates, interpreted through radar profiles, reveals whether a city is balanced, skewed, hard-infrastructure-dominated, soft-capacity-dominated, or structurally weak across multiple fronts. this theoretical lens allows smartness to be operationalized not merely as ranking but as form, pattern, and structural identity.methodologythe analysis uses 91 indicators extracted from two major european data repositories: eurostat's 2025 smart-city datasets and the 2024 urban audit. each indicator corresponds to one of the six smart-city dimensions, forming an extensive database of urban performance covering economy (12 indicators), people (16), governance (12), mobility (10), environment (13), and living (28). to ensure comparability, all data older than 2015 were excluded. after cleaning and standardization, the shannon entropy method was applied to compute dimension-specific weights, ensuring that indicators with greater variation across cities exert proportionally stronger influence. using these weighted scores, six composite values were generated for each city, yielding the coordinates of their smartness geometry. to evaluate relative performance, four multi-criteria decision-making (mcdm) methods were applied independently: ahp, saw, topsis, and vikor. these methods were intentionally selected because they differ in compensability, normalization sensitivity, and aggregation logic. ahp reflects hierarchical expert-based reasoning; saw is fully compensatory and linear; topsis emphasizes distance from ideal and anti-ideal solutions; vikor balances individual and group utility through a compromise model. the friedman test was employed to assess the statistical agreement among the four methods. finally, consensus clustering and radar-geometry analysis were used to classify the cities into geometric types of smartness.results and discussionthe integrated ranking produced a clear hierarchy among european cities. the geometry of smartness across european cities can be interpreted through four distinct typological forms, each representing a structural pattern of urban performance. type t1, the balanced smartness core, reflects cities scoring between 0.70 and 0.96, primarily found in northern and western europe. these cities show strong performance in living standards, mobility, governance, and environmental sustainability, resulting in a symmetrical hexagonal radar chart that signifies equilibrium across all dimensions. type t2, the industrial–economic hardware smartness, includes cities in germany, france, and the united kingdom, typically scoring 0.55-0.70. their radar charts appear as elongated pentagons pulled toward economic, innovation, employment, and infrastructure dimensions, indicating strong hard capacities but less balanced soft dimensions. type t3, the latent software-based smartness, is characteristic of eastern european cities, with scores ranging from 0.45 to 0.55. these cities perform better on people-oriented indicators such as education, governance, and civic participation, while lagging in the economy and mobility, resulting in an asymmetric quadrilateral with elevated human/governance axes and depressed economic ones. finally, type t4, the negative consensus core, includes structurally weak cities of southern europe, positioned between 0.00 and 0.40. their profiles show severe imbalance across all dimensions, forming collapsed or fragmented polygons with sharp recessions that reflect pervasive deficits and the need for significant policy interventions. this typology demonstrates that europe does not move toward a uniform smart-city model but toward differentiated regional patterns—each shaped by historical, economic, cultural, and governance trajectories.conclusionthe study offers a comprehensive analytical device for understanding smart-city performance through a multi-dimensional, geometric, and consensus-based approach. the smartness geometry model reveals that smartness is not simply about technological adoption but about structural harmony across economic, human, institutional, environmental, and infrastructural systems. europe showcases both excellence and disparity: while northern cities achieve equilibrium, southern and eastern cities face multidimensional fragility. the framework developed here is transferable to other regions, provided that a reliable statistical infrastructure is established. without consistent, transparent urban data, neither profiling, geometry, nor benchmarking is possible. strengthening national urban statistics, creating open datasets, and adopting standardized indicators similar to those of the urban audit would allow governments to construct their own smartness geometry. future research should extend this model to comparative regional studies, integrate time-series dynamics, and examine the causal mechanisms behind geometric patterns. the smartness geometry framework thus offers a robust, expandable system for measuring, understanding, and improving urban smartness across diverse global contexts.