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Urban growth occurs in conjunction with a series of decision-making processes and is, on the whole, not deterministic but rather is the outcome of competing local demands and uncontrolled, chaotic processes. Fuzzy sets theory is ideally suited to treat the complexity and uncertainties in the decision-making process. This chapter presented an example of how fuzzy sets can be applied to model urban growth driving forces within geographical information system environment. The mathematical models for measuring, computing and defining 10 fuzzy urban growth factors to form fuzzy driving forces of urban growth in Riyadh City, Saudi Arabia, were discussed. Four factors were considered as the driving forces for urban growth in Riyadh City: the transport support factor, urban agglomeration and attractiveness factor, topographical constraints factor, and planning policies and regulations factor. The urban growth factors were established using fuzzy set theory, which quantified the effect of distance decay using fuzziness. This approach is a transparent method of interpreting the curve of distance decay using linguistic variables. This feature does not exist in the linear, negative exponential or inverse power functions. The results indicate that fuzzy accessibility and fuzzy urban density factors are capable of mimicking and representing the uncertainty in the behaviour of the human decisionmaking process in land development in a very efficient manner.

Modelling Driving Forces of Urban Growth with Fuzzy Sets and GIS