Fuzzy terms in everyday speech

In most basic GIS courses we learn to divide the world into either crisp entities or continuous fields. Queries on the basic spatial entities normally base on the traditional binary logic of "true" or "false", "yes" or "no", 1 or 0, respectively. Let’s look at the terrain characteristic "slope" as one suitability criterion in the wolf habitat analysis. Dividing "slope" into two classes "flat" (s<25°) and "steep" (s>=25°), every single site in space could only be "flat" or "steep". But what about a site ‚A’ with a slope of 25.1°? Is it really appropriate to assigning that site to "steep", knowing that the slope measurement had only a limited accuracy?

Many geographic categorizations apply in such cases modifiers often used in everyday speech. Though, one could introduce an intermediate category such as "moderately" steep" (20°<s<=30°). This would solve the problem for clearly intermediate sites but introduce a new problem cases at the borders of this new interval, e.g. having another site B with 29.2°.

Using Boolean or weighted overlay a location can only fulfil either a query or not fulfil a query. There is no in between, that is a location cannot be both part of the subset "steep" and not part of the subset "steep". A new concept is needed to represent our uncertainty in modelling the environment. Such a new logic should extend our limited binary logic of only "true" and "false" allowing vagueness and uncertainty. This is where the idea of fuzziness enters the overlay story.