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

Abstract

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.

Fire risk evaluation using multicriteria analysis—a case study

“…A detailed review on the basic concepts of fuzzy sets and integration of the same using GIS can be found in Robinson (2003). Integration of fuzzy logic with GIS in a decision-making framework has been used for different purposes, including land suitability based upon soil profiles (Burrough et al 1992), soil classification (Lark and Bolam 1997), landfill site screening (Charnpratheep et al 1997), soil erosion (Mitra et al 1998), crop land suitability analysis (Ahmed et al 2000), ranking burned forests to evaluate the risk of desertification (Sasikala and Petrou 2001), seeking optimum locations for real estate (Zeng and Zhou 2001), assessing vulnerability to natural hazards (Rashed and Weeks 2003;Tangestani 2004;Dixon 2005), estimating risk (Sadiq and Husain 2005), incorporating farmer's knowledge for land suitability classification (Sicat et al 2005), fuel type mapping (Nadeau and Englefield 2006), assessing spatial extent of dry land salinity (Malins and Metternicht 2006), etc.…”

Interpreting spatial language in image captions

“…In between these two extremes, the membership value varies according to a pre-defined membership function and it is the definition of this membership function that is one of the more difficult aspects of fuzzy-approaches, as a balance has to be found between a simpler membership function abstracted from the source data and a complex membership function that is directly derived from the phenomenon. Both approaches have their advantages, as the simpler membership function tend to have better understood behaviour when used with fuzzy operators, while the directly derived function provides a better representation of the vague phenomenon, the decision between the two approaches has to be made on a problem-by-problem basis (see Robinson (2003)). …”

“…Initial approaches to representing vague spatial information computationally were the broad-boundary models (Cohn and Gotts (1996a); Clementini and Felice (1996)). Later fuzzy models were proposed as representations of vague spatial information (Altman (1994);Fisher (2000); Robinson (2000); Schneider (2000)) in order to overcome the simplifications of the broad-boundary models and create a more realistic model of the vague spatial information, but bring with them the problem of how to define the fuzzy membership function (Robinson (2003)). …”

A method to compare and improve land cover datasets: application to the GLC-2000 and MODIS land cover products

“…Fuzzy logic has been used in many remote sensing and GIS applications to address the problem of uncertainty [9]. One of the most common applications has been the use of fuzzy classification of land cover and soil [10], [11].…”