Enhancing a Database Management System for GIS with Fuzzy Set Methodologies Emmanuel Stefanakis and Timos Sellis Knowledge and Database Systems Laboratory Department of Electrical and Computer Engineering National Technical University of Athens Zographou 157 73, Athens, Greece {stefanak, timos}@cs.ntua.gr The methods used in commercial GIS packages for both the representation and analysis of geographic data are inadequate, because they do not handle uncertainty. This leads to information loss and inaccuracy in analysis with adverse consequences in the spatial decision-making process. The incorporation of fuzzy set methodologies into a DBMS repository for the application domain of GIS should be beneficial and will improve its level of intelligence. Focusing on this direction the paper addresses both a representation and a reasoning issue. Specifically, it extends a general spatial data model to deal with the uncertainty of geographic entities, and shows how the standard data interpretation operations available in GIS packages may be extended to support the fuzzy spatial reasoning. Representative geographic operations, such as the fuzzy overlay, fuzzy distance and fuzzy select, are examined, while a real world situation involving spatial decision making is presented. 1. Introduction Uncertainty (sometimes the terms imprecision and vagueness are used instead) refers to the imperfect and inexact knowledge concerning some domain of interest [Goodchild and Gopal, 1989; Openshaw, 1991, Kruse et al., 1991]. The uncertainty is an inherent feature of geographic data and may arise through [Altman, 1994]: a) incomplete information associated to them; b) the presence of varying concentrations of attributes; and c) the use of qualitative descriptions of their attribute values and relationships. Currently used methods for the representation and analysis of geographic information are inadequate, because they do not tolerate uncertainty [Wang et al., 1990]. This is largely due to the underlying membership concept of the classical set theory, according to which a set has precisely defined boundaries and an element has either full or no membership in a given set (Boolean logic). The representation of geographic data based on the classical set theory has a tight effect on reasoning and analysis procedures [Stefanakis, 1997; Stefanakis et al., 1999]. Specifically, the employment of a sequence of basic GIS operations to support a real world situation, such as that of residential site selection, is accompanied with all problems of an “early and sharp classification” [Stefanakis et al., 1999, 1996; Stefanakis, 1997]. The overall decision is made in steps which drastically and sharply reduce the intermediate results. Any constraint is accompanied with an absolute threshold value and no exception is allowed. For instance, if the threshold for a level land is slope = 10%, a location with slope equal to 9.9% is characterized as level, while a second location with slope equal to 10.1% is characterized as non-level (steep). Moreover, for decisions based on multiple criteria, it is usually the case that an entity (i.e., an individual location), which satisfies quite well the majority of constraints and is marginally rejected in one of them, to be selected as valid by decision-makers. However, based on Boolean logic, a location with slope 10.1% will be rejected (as non-level), even if it satisfies quite well all other constraints posed by decision-makers. In addition, decision-makers are obliged to express their constraints through arithmetical terms and mathematical symbols in crisp relationships (e.g., slope < 10%), since they are not allowed to use natural language lexical terms (e.g., level land). Finally, another effect of classical set theory is that the selection result is flat, in the sense that there is no overall ordering of the valid entities as regard to the degree they fulfill the set of constraints. For instance, dry-level layer highlights all locations which satisfy the constraints: dry land (threshold 20%) and Proceedings of the 19 th International Cartographic Conference, Ottawa, Canada, August 1999.