A Perspective on the Fundamentals of Fuzzy Sets and their Use in Geographic Information Systems

The development of fuzzy sets in geographic information systems (GIS) arose out of the need to handle uncertainty and the ability of soft computing technology to support fuzzy information processing. An overview of the fundamentals of fuzzy sets is used to illustrate its use in GIS. The use of some terms within both the GIS and fuzzy information processing community is clarified. Since one of the key problems when applying fuzzy sets to GIS problems is in the specification of grades of membership, the many methods used to specify memberships in fuzzy sets in GIS applications are presented. The α cut is defined and shown to be of increasing importance in GIS. Non-compensatory and compensatory connectives are compared. Aggregation operators are reviewed and shown to be useful in a number of GIS studies. Fuzzy relations and fuzzy control systems are briefly discussed with reference to their use in GIS and in relation to the development of modern soft computing technology. Several features of fuzzy sets make that paradigm attractive for use in GIS. It is concluded that as GIS-related applications increase in their levels of complexity and sophistication fuzzy sets will play a major, cost effective role in their development.