Investigating the Impact of Urbanization Rate Uncertainty and Hydroelectric Energy Consumption on Ecological Footprint in Iran; Fuzzy Regression Approach

Abstract
Introduction
The ecological footprint serves as a valuable indicator for assessing anthropogenic pressures on ecosystems and the environment. Given its significance, this study investigates the impact of uncertainty in urbanization rates and hydropower energy consumption on Iran’s ecological footprint, while also examining the effects of natural resource rents, per capita income, and industrial production. A fuzzy regression model is employed to analyze these relationships over the period 1970-2022. By leveraging the capabilities of fuzzy regression modeling, the intensity of each determinant's influence is quantified in terms of the center, left spread, and right spread of fuzzy sets. Under conditions of high uncertainty—represented by a membership degree of 0.9—the right spread results indicate that urbanization growth is the primary driver of ecological footprint expansion, highlighting the need for green urban technologies. Natural resource rents exert a significant impact, necessitating optimal management strategies. The effect of per capita income varies depending on prevailing consumption patterns, while industrial production increases the ecological footprint primarily through energy-intensive processes, underscoring the importance of adopting clean technologies. Hydropower consumption ranks third in terms of ecological impact, suggesting that even renewable energy sources may entail environmental trade-offs when deployed at scale. In this context, renewable energies—valued for their environmental compatibility, non-polluting nature, renewability, and global availability—are particularly attractive, especially for developing countries pursuing sustainable development pathways.
Introduction
Urbanization, one of the most defining phenomena of the modern era, has attracted considerable attention from policymakers and researchers in recent decades due to its profound economic and social implications. This process involves the migration of populations and labor from rural areas and agricultural sectors to urban centers, driven by the search for employment in industrial and urban-based occupations. Concurrently, environmental degradation resulting from human activities has emerged as a critical global challenge, with significant impacts not only on ecosystems and natural resources but also on economic outcomes. In response, clean energy has become a cornerstone of sustainable development strategies, valued for its environmental compatibility and now deeply integrated into national energy planning and policy frameworks.
At the macroeconomic level, decision-making under uncertainty has been widely studied, as unpredictable conditions complicate long-term planning and shape economic behavior. Key sources of such uncertainty include shifts in government policies and fluctuations in macroeconomic indicators. The interplay between rapid urbanization and hydropower energy consumption presents a dual challenge for sustainable development: while expanding cities require a reliable and scalable energy supply, maintaining ecological balance remains imperative. Against this backdrop, this paper investigates the impacts of urbanization rates and hydropower energy consumption on the ecological footprint and proposes policy-oriented strategies to optimize sustainability trajectories.
Methods and Materials
Annual data required to assess the impact of uncertainty in urbanization rates and hydropower energy consumption on Iran’s ecological footprint were collected for the period 1970-2022. A fuzzy regression approach was employed, with model estimation performed using MATLAB software. This method derives the optimal regression equation by minimizing the overall level of fuzziness—specifically, by reducing the total width of the fuzzy membership functions associated with the regression coefficients.
Fuzzy regression models differ fundamentally from classical regression techniques. Traditional regression relies on strict statistical assumptions, including normality of errors, absence of autocorrelation, and homoscedasticity (constant error variance). In contexts where these assumptions are difficult to satisfy—particularly when data are imprecise, ambiguous, or subject to uncertainty—fuzzy regression provides a robust and insightful alternative. It represents uncertainty through possibility distributions and membership functions, thereby accommodating vagueness in both data and relationships without requiring probabilistic error structures
Results and Discussion
The analysis of the effects of uncertainty in hydropower energy consumption, urbanization rates, natural resource rents, per capita income, and industrial production on Iran’s ecological footprint was conducted using fuzzy regression concepts—specifically, membership degree and the left spread, center, and right spread of fuzzy sets. Membership degrees of 0.1 and 0.9 represent conditions of reduced and increased influence, respectively, of the aforementioned factors on the ecological footprint. Under high-uncertainty conditions (membership degree = 0.9), the right fuzzy spread estimates yield coefficients of 1.244, 2.851, 1.898, 0.657, and −3.6447×10⁻¹⁶ for hydropower consumption, urbanization, natural resource rents, per capita income, and industrial production, respectively—indicating their substantial and mostly positive contributions to ecological footprint expansion. Conversely, the left fuzzy spread results are −1.244, −2.851, −0.715, −0.657, and −3.6447×10⁻¹⁶, reflecting the lower bounds of these impacts under reduced uncertainty (membership degree = 0.1).
Existing domestic and international studies—reviewed in the literature—have typically examined the determinants of the ecological footprint (e.g., urbanization, hydropower use, carbon emissions, and economic growth) using classical econometric methods such as ordinary least squares (OLS) or panel regression. These approaches estimate single-point coefficients and rely on precise, deterministic data. However, such models require complete and unambiguous information due to structural assumptions, including error normality, homoscedasticity, and the absence of measurement error—conditions often violated in sustainability-related analyses.
In contrast, this study employs fuzzy regression, which offers greater flexibility in modeling uncertain and imprecise systems. Rather than producing a single estimated value for each parameter, fuzzy regression generates a fuzzy output characterized by the center, left spread, and right spread, thereby capturing the full range of possible impacts under varying degrees of uncertainty. Moreover, by incorporating the concept of membership degree, this approach explicitly accounts for ambiguity in both data and relationships. Consequently, fuzzy regression demonstrates superior distributive power and robustness in ecological footprint analysis, particularly when dealing with volatile, incomplete, or inherently uncertain socioeconomic and environmental variables.
Conclusion
This study specifically investigates the impact of uncertainty in urbanization rates and hydropower energy consumption on Iran’s ecological footprint, while also accounting for the effects of natural resource rents, per capita income, and industrial production. To address the inherent imprecision in these variables, a fuzzy regression model with symmetric coefficients—known for its high modeling flexibility—was employed. The analysis draws on standard fuzzy regression concepts, namely the fuzzy center, right spread, and left spread, to characterize the behavior and influence of each explanatory variable.
This modeling approach provides valuable insights for national policymaking, offering a robust framework to inform sustainable development strategies and guide planners in managing environmental pressures. The results indicate that the fuzzy center, right spread, and left spread represent, respectively, the average, maximum, and minimum effects of the selected determinants on Iran’s ecological footprint. Specifically, under conditions of high uncertainty (membership degree = 0.9), the right fuzzy spread yields coefficients of 1.244 (hydropower consumption), 2.851 (urbanization), 1.898 (natural resource rents), 0.657 (per capita income), and −3.6447×10⁻¹⁶ (industrial production). Conversely, the left fuzzy spread—reflecting lower-bound impacts—produces values of −1.244, −2.851, −0.715, −0.657, and −3.6447×10⁻¹⁶ for the same variables, respectively. These findings highlight the asymmetric and uncertain nature of the relationships between key socioeconomic drivers and environmental pressure in Iran.