The use of Rough Set and Spatial Statistic in evaluating the Periurban Fringe

The distinction among urban, peri-urban and rural areas inside a territory represents a classical example of uncertainty in land classification. The transition among the three classes is not much clear and can be described with Sorites Paradox, considering the residential buildings and the settlements. Peri-urban fringe can be considered as a transition zone between urban and rural areas, as an area with its own intrinsic organic rules, as a built area without formal organisation or as an abandoned rural area contiguous to urban centres. In any case, concepts as density of buildings, services and infrastructures or the degree of rural, residential and industrial activities, will lead to uncertainty in defining classes, due to the uncertainty in combining some properties. One of the methods which can be utilized is the rough sets theory, which represents a different mathematical approach to uncertainty capturing the indiscernibility. The definition of a set is connected to information knowledge and perception about phenomena. Some phenomena can be classified only in the context of the information available about them. Two different phenomena can be indiscernible in some contexts and classified in the same way (Pawlak 83). The rough sets approach to data analysis hinges on two basic concepts, the lower approximation which considers all the elements that doubtlessly belong to the class, and the upper approximation which includes all the elements that possibly belong to the class. The rough sets theory furthermore takes into account only properties which are independent. This approach has been tested in the case of study of Potenza Province. This area, located in Southern Italy, is particularly suitable to the application of this theory, because it includes 100 municipalities with different number of inhabitants, quantity of services and distance from the main road infrastructures.