Introduction 
As one of the most fundamental areas in economic and social development, the housing sector requires a precise analysis of supply and demand factors. This study helps policymakers prevent crises through optimal management and design residential projects aligned with societal needs. Additionally, understanding the factors influencing this sector aids in forecasting future housing market trends and enables better decision-making for investors. Economic uncertainty, particularly during crisis periods, has significantly impacted the housing market in recent years. This uncertainty has affected variables such as inflation rates, interest rates, and housing prices, causing severe fluctuations in the market. Furthermore, a complex relationship between the stock market and the housing market influences investor behavior under uncertain conditions, potentially leading to shifts in investment towards or away from the housing market.
This research investigates the impact of uncertainty on the housing price index and the role of the stock market index in Iran from 1991 (1370) to 2023 (1402). This study also analyzes variables such as bank interest rate, inflation, exchange rate, per capita income, and urbanization. The main hypotheses focus on the significant influence of the stock market index and exchange rate on housing prices. The results of this study can assist policymakers in controlling housing market fluctuations.
Materials and Methods
This study examines the impact of uncertainty in key factors affecting the housing price index, emphasizing the stock market index. Key variables include national income, bank interest rate, urbanization rate, inflation, exchange rate, and the stock market index, selected based on previous studies. Annual data were collected from the Central Bank of Iran (1991–2023) and analyzed using fuzzy regression in MATLAB software. Unlike classical methods, fuzzy regression quantifies ambiguity in data and models using triangular membership functions. This method is suitable for situations where data are insufficient, non-normal, or relationships between variables are ambiguous.
In this study, an asymmetric fuzzy regression model was used, allowing for the calculation of left and right widths of coefficients, thereby providing a more accurate depiction of uncertainty’s impact. Fuzzy logic, unlike classical logic, accepts ambiguity as part of the system and describes it with values between zero and one. This approach supports modeling real-world conditions accompanied by uncertainty. In this research, fuzzy coefficients were estimated asymmetrically to provide greater flexibility in analyzing variable impacts. The primary objective was to estimate the impact of uncertainty on the housing price index at a membership degree of 0.9, indicating a high level of ambiguity. Each fuzzy coefficient includes a core value (average effect) and left and right widths (minimum and maximum effects). This method assists policymakers in making better decisions when facing housing market fluctuations. The results of this study could play a crucial role in managing housing price volatility by more accurately analyzing influencing factors under uncertainty. Moreover, comparing the impact of the stock market index and exchange rate on housing prices can help investors and economic planners design more effective strategies. Ultimately, this research demonstrates that fuzzy regression is a powerful tool for analyzing volatile markets like housing, as it can model inherent ambiguity in economic variables. The findings of this study can serve as a foundation for future research and economic policymaking.
Findings
Using a fuzzy regression model (membership degree of 0.9), this study investigated the impact of uncertainty in factors affecting the housing price index, particularly the stock market index. Thirty-two years of annual data (1991–2023) from the Central Bank of Iran were analyzed in MATLAB with 64 constraints. The results show that the right and left widths of fuzzy coefficients indicate the maximum and minimum effects of variables on housing prices, while the fuzzy center represents the average effect. Urbanization rate had a positive and significant impact with a fuzzy center of 0.0034 and equal right and left widths (0.0226), reflecting high demand due to urban population growth. Conversely, the bank interest rate (center: 0.0071) showed a dual effect: the right width (0.0130) predicted price increases, while the left width (-0.0128) forecasted decreases, likely due to unattractive real interest rates in Iran.
The stock market index had the highest impact with a fuzzy center of 0.0662, but its right width (0.3752) indicated the potential for drastic housing price increases. This relationship is explained through substitution effects (negative), wealth effects (positive), and credit expansion effects (positive). Additionally, the exchange rate had a much stronger influence with a center of 0.6829 and a right width of 2.8586, attributed to rising construction costs and foreign demand. Inflation positively affected housing prices with a constant coefficient of 0.1545, as it reduces housing supply and increases construction costs. Per capita income showed limited influence with a center of 0.0018 and a right width of 0.0087. Research charts suggest that if uncertainty remains uncontrolled, housing prices will move toward the right (sharp increase). Findings confirm that exchange rate, stock market index, and inflation are among the key factors driving housing price fluctuations in Iran. This study emphasizes the need for policy interventions to reduce uncertainty in these variables and prevent excessive price increases. The results can aid policymakers in designing sustainable strategies for the housing market.
Conclusion
Using a fuzzy regression model (membership degree of 0.9), this study investigated the impact of uncertainty in factors affecting the housing price index, focusing on the stock market index. A key advantage of this method is its ability to prioritize variables and measure their range of influence (through fuzzy center, right width, and left width). Results showed that the stock market index had the highest impact with a fuzzy center of 0.0662 and a right width of 0.3752. Meanwhile, the exchange rate was identified as the strongest factor driving housing price fluctuations, with a center of 0.6829 and a right width of 2.8586. These findings align with previous studies such as Jafari Samimi (2007) and Al-Rifai (2021). Fuzzy width analysis shows that increasing uncertainty will push the housing price index toward maximum values (right width), while controlling uncertainty can guide it toward lower levels (left width). This indicates that current housing market volatility stems from instability in macroeconomic variables such as exchange rate, inflation (with a constant coefficient of 0.1545), and the stock market index. Also, the dual effects of bank interest rate (right width: 0.0130, left width: -0.0128) and the limited role of per capita income (center: 0.0018) emphasize the need for careful policymaking in these areas. Given the strong dependence of housing prices on financial and exchange rate variables, it is recommended that policymakers focus on housing supply (e.g., facilitating construction) and demand regulation (e.g., attractive bank interest rates) to balance the market. Additionally, developing innovative financial instruments in the stock market (e.g., real estate investment funds) could both reduce housing demand and provide financial resources for construction development. Overall, this study highlights the necessity of managing uncertainty in macroeconomic variables, especially the exchange rate and stock market index, as catalysts for housing price fluctuations. It is recommended that the government restore stability to the housing market through coordinated monetary, exchange rate, and fiscal policies, utilizing fuzzy tools for continuous monitoring of uncertain factors. This approach not only prevents excessive price increases but also facilitates balanced development in the housing sector.