Even with much activity over the past decade, including organized efforts on both sides of the Atlantic, the representation of both space and time in digital databases is still problematic and functional space-time systems have not gone beyond the limited prototype stage. Why is this the case? Why did it take twenty years from the ®rst GIS for the for representation and analysis in the temporal, as well as the spatial dimension, to begin? I explore the answers to these questions by giving a historical overview of the development of space-time representation in the geographic information systems and database communities and a review of the most recent research. Within the context of this perspective, I also question what seems to be a spirit of self-accusation in which the lack of functional space-time systems has been discussed in the literature and in meetings of GIS researchers. I close by offering my own interpretation of current research issues on space-time data models and languages.

Predictive soil mapping (PSM) can be defined as the development of a numerical or statistical model of the relationship among environmental variables and soil properties, which is then applied to a geographic data base to create a predictive map. PSM is made possible by geocomputational technologies developed over the past few decades. For example, advances in geographic information science, digital terrain modeling, remote sensing, fuzzy logic has created a tremendous potential for improvement in the way that soil maps are produced. The State Factor soil-forming model, which was introduced to the western world by one of the early Presidents of the American Association of Geographers (C.F. Marbut), forms the theoretical basis of PSM. PSM research is being driven by a need to understand the role soil plays in the biophysical and biogeochemical functioning of the planet. Much research has been published on the subject in the last 20 years (mostly outside of geographic journals) and methods have varied widely from statistical approaches (including geostatistics) to more complex methods, such as decision tree analysis, and expert systems. A geographic perspective is needed because of the inherently geographic nature of PSM.

Presettlement forest types were mapped as fuzzy sets from point data representing trees contained in General Land Office survey notes (ca.1850) for Chippewa County, Michigan. The resulting representation agreed with a polygon map of the same forest types at 66 percent of the locations (represented as grid cells) in the county. Boundary vagueness was defined in relation to the slope of a linear function fitted to the negative relationship between entropy of forest types and distance to polygon boundaries. The similarity between forest type compositions (i.e., classification ambiguity) was shown to account for 55 percent of the variation in boundary vagueness.

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. At present, Geographic Information Systems (GIS) though powerful toolboxes, most with hundreds of functions, they suffer from several limitations which render them inefficient tools for spatial decisionmaking. This paper focuses on the inappropriate logical foundation incorporated into them and examines the necessity of adopting fuzzy logic methodologies in GIS operations. 1 Introduction Geographic Information Systems (GIS) are computer-based systems designed to support the capture, management, manipulation, analysis, modeling and display of spatially referenced data at different points in time [1]. Today, GISs are widely used in many government, business and private activities; which fall into three major categories [10]: a) socio-economic applications (e.g., urban and regional planning, cadastrial registration, archaeology, natural resources, etc.); b) environmental applications (e.g., forestry, fire and epidemic control, etc.); and c) management applications (e.g., organization o...

Data on tree location and species in a portion of Northern Michigan were gathered from General Land Office (GLO) survey notes (ca. 1850), digitized, and generalized to represent forest types. Fuzzy membership values describing the degree of membership of each species in each forest type were derived from (a) semantic information in the forestry literature and (b) a fuzzy clustering routine applied to data from randomly placed circular plots. The fuzzy membership values assigned to each tree point for each forest type were interpolated to form continuous surfaces using kriging and co-kriging. Advantages of this method over traditional discrete mapping methods include: (a) multiple options are available for the display and analysis; (b) classification uncertainty and the continuity of natural vegetation can be represented; and (c) the classification scheme is applied systematically across the entire map area and can be altered to produce alternative maps. The subset of available display and analytical products presented include: discrete forest type maps; a surface representing the confusion between forest types; fuzzy logical overlays of forest types; and discrete class maps with color value altered within each class to indicate degree of confusion at each location.

For some spatiotemporal applications, it can be assumed that the modeled world is precise and bounded, and that also our record of it is precise. While these simplifying assumptions are sufficient in applications like a land information system, they are unnecessarily crude for many other applications that manage data with spatial and/or temporal extents, such as navigational applications. This work explores fuzziness and uncertainty, subsumed under the term indeterminacy, in the spatiotemporal context. To better illustrate the basic spatiotemporal concepts of change or evolution, it is shown how the fundamental modeling concepts of spatial objects, attributes, and relationships and time points and periods are influenced by indeterminacy and how they can be combined. In particular, the focus is on the change of spatial objects and their geometries across time. Four change scenarios are outlined, which concern discrete versus continuous change and asynchronous versus synchronous measurement, and it is shown how to model indeterminacy for each. A case study illustrates the applicability of the paper’s general proposal by describing the uncertainty related to the management of the movements of point objects, such as the management of vehicle positions in a fleet management system.

Land evaluation is the process of predicting the use potential of land on the basis of its attributes. A variety of analytical models can be used in these predictions, ranging from qualitative to quantitative, functional to mechanistic, and specific to general. This paper classifies land evaluation models by how they take time and space into account, and whether they use land qualities as an intermediate between land characteristics and land suitability. Temporally, models can be of a static resource base and static land suitability, a dynamic resource base but static land suitability, or both a dynamic resource base and dynamic land suitability. Spatially, land evaluation models can be of a single area with no interaction between areas, with static inter-area effects, or dynamic inter-area effects. In the most complex case, land suitabilities for several land uses are interdependent.

ABSTRACT: The paper focuses on two large application areas of the Fuzzy Set Theory in ecological research, namely data analysis (in particular fuzzy cluster analysis and fuzzy kriging) and ecological modelling. Environmental data or classes of ecological objects can be defined as fuzzy sets with not sharply defined boundaries, that reflects better the continuous character of nature. Fuzzy sets are used to handle uncertainty of data environmental data and fuzzy logic to handle inexact reasoning in knowledge-based modells of ecological processes. Some application examples of data analysis (fuzzy classification and fuzzy regionalization) and knowledge-based modelling are presented.

Cellular automata (CA) are discrete systems used for modelling complex spatial dynamic phenomena. The discrete nature of CA enables integration with rasterbased geospatial datasets in geographic information systems (GIS), and also can be beneficial when modelling complex ecological processes that evolve over time. However, when modelling forest insect infestations it is difficult to use discrete cell states to represent, for example, the concept of susceptibility of a tree to insect attack. The use of binary or probabilistic approaches for cell states definition is not appropriate because insect disturbances are driven by numerous components of insect-tree relationships that are difficult to understand. Furthermore, uncertain transition zones exist between forest stands of different sizes and different species where a discrete definition of a cell cannot be provided. The objective of this study was to integrate fuzzy set theory with GISbased CA modelling to model tree mortality patterns caused by insect infestation, and to explore the sensitivity of the model to different spatial properties. This study focused on a case study of lodgepole pine, Pinus contorta, mortality patterns caused by infestations of mountain pine beetle (MPB), Dendroctonus ponderosae Hopkins. The use of fuzzy set theory addresses the issue of inherent uncertainty of the geospatial data used for studies of forest infestations, while a test of model sensitivity explores the influence of the spatial properties of a fuzzy-constrained CA. 1.