In general, classification methods allow you to reduce the dimensionality of a complex data set by grouping the data into a set number of classes.
With traditional (crisp) classification methods, each sample/location is placed into one class or another. In crisp classification, class membership is binary, a sample is a member of a class or not. Crisp class membership values can be either "1" when that class is the best fit, or "0" (for all other classes).
In fuzzy classification, a sample can have membership in many different classes to different degrees. Typically, the membership values are constrained so that all of the membership values for a particular sample sum to 1.
Fuzzy classes are appropriate for continuous data that does not fall neatly into discrete classes, such as climatic data (McBratney and Moore 1985), vegetation type (Lowell 1994, Brown 1998a) soil classification (McBratney and deGruijter 1992), and many other engineering, geological, and medical applications (reviewed in Bezdek 1987). Fuzzy classes can better represent transitional areas than hard classification (Brown 1998a), as class membership is not binary (yes/no) but instead one location can belong to a few classes.
Brown (1998) identifies fuzzy classification as appropriate for data with 1) "attribute ambiguity" and 2) "spatial vagueness." Attribute ambiguity occurs when class membership is partial or unclear. Ambiguity is particularly a problem for some remotely-sensed data, such as aerial photography, which is not interpreted consistently (Edwards and Lowell 1994, cited in Lowell 1994). Spatial vagueness emerges when the sampling resolution is not fine enough to catch boundary locations, when gradual transitions occur between classes, or when there is some location uncertainty in the data.
Fuzzy classes depict the spatial and attribute uncertainty present in most data sets more accurately than hard classification.
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