Boundary Analysis and Fuzzy Logic

A significant part of the study is to determine the boundaries and the rate of change within each of the variables, between the forest and the clear-cut. This boundary analysis is a tool for investigating 'edge effects' which are differences in ecological processes that occur at or near ecosystem or habitat boundaries (Jacquez, et al., 1999). Traditionally we have boundaries as crisp lines that surround homogeneous areas whether it be mapping out administrative units in Vancouver or swamps in North Dakota, we use the same techniques to show the border between one object class and another. As well, within these borders we assume homogeneity, therefore, because we are studying soil properties it should be known that within the "homogeneous" areas at every level of resolution, at least down to the individual clay particle, variations will occur. This can be explained in terms of a natural process of transport, erosion or chemical change (Burrough, 1996).

The areas concerning human made objects tend to be better defined. The boundary between a building and a field or BC and Alberta or a forest and a clear-cut is crisp as shown in the photos. The clear-cut has a well-defined boundary. We can visually see the dramatic change from forest to clear-cut. The problem arises when we wish to use this boundary to make conclusions about soil property variations.

As mentioned before, variations will occur within the soil. This is because the nature of the soil data is continuous and can not be easily discretized into nice clean spatial objects. These imprecisely defined classes are called fuzzy sets (Cheng and Molenaar, 1999). Fuzzy sets admit the possibility of continuous partial membership. That means, a point along or near an edge can belong to several classes.