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Brimicombe, A.J. (2009) GIS, Environmental Modeling and Engineering (2nd Edition). CRC Press, Boca Raton, FL, USA.

Brimicombe, A.J. (2003) GIS, Environmental Modelling and Engineering. Taylor & Francis, London. 

The significance of modelling in managing the environment is well recognised from scientific and engineering perspectives as well as in the political arena. Environmental concerns and issues of sustainability have permeated both public and private sectors, particularly the need to predict, assess and mitigate against adverse impacts that arise from continuing development and use of resources. Environmental modelling is an inherently spatial activity well suited to taking advantage of Geographical Information Systems (GIS) functionality whether this be modelling aspects of the environment within GIS or linked to external simulation models. In doing so, a number of issues become important: environmental models need to consider space-time processes often in three-dimensions whereas GIS are largely two-dimensional and static; environmental models are often computational simulations, as distinct from cartographic modelling and map algebra in GIS; what should be the degree of integration between GIS and environmental models on any project; how does uncertainty in spatial data from GIS and the choices of parameterisation in environmental models combine and propagate through analyses to affect outputs; by what means can decisions be made with uncertain information. These issues inevitably arise in every scientific and engineering project to model and manage our environment. Students need to be made aware of these issues. Practitioners should enrich their knowledge and skills in these areas. This book focuses on the modelling, rather than on data collection or visualisation - other books adequately cover these areas - and aims to develop critical users of both GIS and environmental models.

Brimicombe, A.J. (2000) "Processus de décision en géoéconomie dans un contexte imprécis et incertain" (with Billot, Frankhauser, Josselin, Nicot & Rolland-May) Revue Française de Géoéconomie 13: 161-179 

Brimicombe, A.J. (2000) "Encoding expert opinion in geo-information systems: a fuzzy set solution" Transactions in International Land Management 1: 105-121 

Since much of the relevant information will be derived from digital spatial data, geo-information systems (GIS) and related IT will be key tools. An area where these tools currently perform poorly is in the encoding, storage and analytical handling of expert opinion or linguistic statements regarding the data content of GIS. This paper proposes a solution - fuzzy expectation (˜E). Fuzzy expectation is derived from a small number of stylised fuzzy sets which, using an intuitive probability interface, are building blocks for 'translating' expert opinion into a compact fuzzy set representation. Once encoded, expert opinion about the data is embedded in the data structure and can be combined and propagated through GIS analyses such as overlay. A worked example in a land management context is provided as a means of illustrating the implementation of ˜E.

Brimicombe, A.J. (1998) "A fuzzy set approach to using linguistic hedges in geographical information systems" CyberGEO - European Journal of Geography 

Brimicombe, A.J. (1998) "A fuzzy co-ordinate system for locational uncertainty in space and time", Innovations in GIS 5 (ed. Carver), Taylor & Francis: 143-152 

Uncertainty is an unavoidable characteristic of thematic maps derived from digital spatial data. Boundaries drawn as pixel-thin lines to universally represent sharp, gradual or vague changes in a theme are an inevitable consequence of the lack of stored data with which to interpret these boundaries otherwise. Although some recent research has focused on the uncertainty of boundaries deriving from the purity of the polygons on either side, there is scope for explicitly recording the locational extent of uncertainty for individual points and lines that make up polygon boundaries. Fuzzy numbers are introduced and used to construct a fuzzy co-ordinate system in two-, three- and four-dimensions. The paper discusses the geometry of fuzzy lines and their inclusion within the traditional GIS topological data structure. By using a C language struct, the overhead of including data on boundary uncertainty may be minimal. Fuzzy number co-ordinate geometry offers opportunities in GIS applications where boundaries are inherently inexact to have more representative data that better reflect the true situation.

Brimicombe, A.J. (1997)"A universal translator of linguistic hedges for the handling of uncertainty and fitness-for-use in Geographical Information Systems" in Innovations in GIS 4 (ed. Kemp), Taylor & Francis: 115-126

Spatial data quality has been attracting much interest. Much of the problem lies in the degree to which current data structures are unable to model the real world and the way imperfections in the data may propagate during analyses and cast doubt on the validity of the outcomes. Much of the research has concentrated on the quantitative accuracy of spatial data, the derivation of indices and their propagation through analyses. Geographical data invariably includes an element of interpretation for which linguistic hedges of uncertainty may be generated. The paper presents a new technique of handling such expressions in a GIS through fuzzy expectation - intuitive probabilities linked to stylized fuzzy sets. This can be achieved without adversely affecting the size of the database. By using fuzzy expectation as linguistic building blocks, many of the difficulties in using fuzzy set descriptors in GIS have been overcome. The stylized fuzzy sets can be propagated using Boolean operators to give a resultant fuzzy set which can be 'translated' back into a linguistic quality statement. For the first time, linguistic criteria of fitness-for-use can be derived for GIS outputs regardless of the language being used.

Brimicombe, A.J. (1993) "Combining positional and attribute uncertainty using fuzzy expectation in a GIS" Proceedings GIS/LIS'93, Minneapolis, Vol. 1: 72-81

Spatial data of natural resources and other aspects of the environment are frequently inexact with levels of inherent and perceived uncertainty. The literature mostly treats positional and attribute uncertainty separately. A model has been developed which provides the basis for recording uncertainty, for propagation of uncertainty during data transformation and for assessing fitness-for-use of outcomes. In the context of this model, a metric - fuzzy expectation - has been developed as an extension of fuzzy sets and fuzzy numbers into a coordinate system and linguistic uncertainty descriptor. Using this metric, thematic uncertainty can be modeled over vague boundaries.