This article presents a new methodology for urban growth modeling by integrating cellular automata (CA) and genetic fuzzy algorithms. The urban growth phenomenon is a spatio‐temporal and continuous process that can be modeled by employing fuzzy logic as a framework for handling vagueness. Dependence upon an expert for assigning membership functions and rule weights has made the fuzzy logic approach rather subjective. Our proposed methodology overcomes this shortcoming by applying genetic algorithms to tune and optimize the fuzzy logic system and to make it expert independent. The optimization process encompasses a fuzzy membership function and weights for fuzzy rules. This model uses linguistic variables for defining CA transition rules and applies them to represent the non‐deterministic nature of urban growth. The proposed model is applied to simulate urban growth in the Tehran Metropolitan Area in Iran across time steps of 1988, 1999, and 2010 developed using Landsat TM and ETM+ images and a Digital Elevation Model. The first data pairs were employed for calibration of the model parameters, and the remainder of the data was used for validation of the model across time. The model was evaluated using a relative operating characteristic of 0.88 and a figure of merit statistic of 0.31, which quantifies the model goodness of fit.

ABSTRACT:Urban growth phenomenon as a spatio-temporal continuous process is subject to spatial uncertainty. This inherent uncertainty cannot be fully addressed by the conventional methods based on the Boolean algebra. Fuzzy logic can be employed to overcome this limitation. Fuzzy logic preserves the continuity of dynamic urban growth spatially by choosing fuzzy membership functions, fuzzy rules and the fuzzification-defuzzification process. Fuzzy membership functions and fuzzy rule sets as the heart of fuzzy logic are rather subjective and dependent on the expert. However, due to lack of a definite method for determining the membership function parameters, certain optimization is needed to tune the parameters and improve the performance of the model. This paper integrates genetic algorithms and fuzzy logic as a genetic fuzzy system (GFS) for modeling dynamic urban growth. The proposed approach is applied for modeling urban growth in Tehran Metropolitan Area in Iran. Historical land use/cover data of Tehran Metropolitan Area extracted from the 1988 and 1999 Landsat ETM + images are employed in order to simulate the urban growth. The extracted land use classes of the year 1988 include urban areas, street, vegetation areas, slope and elevation used as urban growth physical driving forces. Relative Operating Characteristic (ROC) curve as an fitness function has been used to evaluate the performance of the GFS algorithm. The optimum membership function parameter is applied for generating a suitability map for the urban growth. Comparing the suitability map and real land use map of 1999 gives the threshold value for the best suitability map which can simulate the land use map of 1999. The simulation outcomes in terms of kappa of 89.13% and overall map accuracy of 95.58% demonstrated the efficiency and reliability of the proposed model.