Fuzzy regions: Theory and applications

Traditionally, information in geographic information systems (GIS) is represented as crisp information. While for many applications, this is a good enough approximation of reality, some models would benefit from having the inherent imprecision or uncertainty incorporated in the model. In literature, several ideas and concepts to improve on the crisp models have been considered. In the past, we have presented different models to represent and to work with the concept of regions, defined using fuzzy set theory in GIS systems. For such fuzzy regions, a number of approaches already have been described in detail. In this paper, we will elaborate on a fuzzy set approach and practical implementations of the concept. Apart from the concept, two developed techniques (one based on triangulated networks, one based on bitmap models) are presented along with some of the operators. An overview of application fields is provided to illustrate where and how the techniques can be used.Traditionally, information in geographic information systems (GIS) is represented as crisp information. While for many applications, this is a good enough approximation of reality, some models would benefit from having the inherent imprecision or uncertainty incorporated in the model. In literature, several ideas and concepts to improve on the crisp models have been considered. In the past, we have presented different models to represent and to work with the concept of regions, defined using fuzzy set theory in GIS systems. For such fuzzy regions, a number of approaches already have been described in detail. In this paper, we will elaborate on a fuzzy set approach and practical implementations of the concept. Apart from the concept, two developed techniques (one based on triangulated networks, one based on bitmap models) are presented along with some of the operators. An overview of application fields is provided to illustrate where and how the techniques can be used.P