Fuzzy Sets

Not all uncertainty in spatial data relates to error. A very common source of uncertainty in categorical geospatial data is that of fuzzy sets. Fuzzy sets are classifications in which the boundaries between classes are not distinct. For example, if you categorize slopes into two classes, steep and shallow, how precise are the defnitions of steep and shallow? If slopes greater than 20% are steep, does it mean that those of 19.9999% are not steep?

With fuzzy sets, a membership function for each class is defined. The function takes on values between 0 and 1 in order to measure the grade of membership (known as possiblity) a particular entity has in that class. For instance, a slope of 15% might have a membership grade of 0.22 for steepness while a slope of 20% might have a membership grade of 0.78.

This description of fuzzy sets was excerpted from Dawn Wright's course materials for Introduction to GIS, GEO 465/565 at Oregon State University, Topic on Error & Uncertainty in Databases. http://dusk.geo.orst.edu/gis/

Fuzzy membership grades can be incoporated into the database as a form of feature-level or embedded metadata.

More information on how fuzzy sets are used to assess uncertainty in spatial data is dealth with in:

Kennedy, M. 2000. Embedded metadata - quality control with the dot probability paradigm and ArcQC. Proceedings of the Twentieth Annual ESRI User Conference. View full paper

An interesting example of how fuzzy set theory is applied to metadata, in order to assist in the selection, definition and management of geospatial data:

Vert, G.L. 2000. A fuzzy object relational model for the management of spatial data. Ph.D. thesis, University of Idaho, 234 pp. View abstract

Another fuzzy set reference:

Sui, D.Z. 1994. Fuzzy logic can help GIS cope with reality. GIS World 7(9): 50-53.