An abstract data type to handle vague spatial objects based on the fuzzy model

Crisp spatial data are geometric features with exact location on the extent and well-known boundaries. On the other hand, vague spatial data are characterized by inaccurate locations or uncertain boundaries. Despite the importance of vague spatial data in spatial applications, few related work indeed implement vague spatial data and they do not define abstract data types to enable the management of vague spatial data by using database management systems. In this sense, we propose the abstract data type FuzzyGeometry to handle vague spatial data based on the fuzzy model. FuzzyGeometry was developed as a PostgreSQL extension and its implementation is open source. It offers management for fuzzy points and fuzzy lines. As a result, spatial applications are able to access the PostgreSQL to handle vague spatial objects.FAPESPCAPESCNP

Towards development of fuzzy spatial datacubes : fundamental concepts with example for multidimensional coastal erosion risk assessment and representation

Les systèmes actuels de base de données géodécisionnels (GeoBI) ne tiennent généralement pas compte de l'incertitude liée à l'imprécision et le flou des objets; ils supposent que les objets ont une sémantique, une géométrie et une temporalité bien définies et précises. Un exemple de cela est la représentation des zones à risque par des polygones avec des limites bien définies. Ces polygones sont créés en utilisant des agrégations d'un ensemble d'unités spatiales définies sur soit des intérêts des organismes responsables ou les divisions de recensement national. Malgré la variation spatio-temporelle des multiples critères impliqués dans l’analyse du risque, chaque polygone a une valeur unique de risque attribué de façon homogène sur l'étendue du territoire. En réalité, la valeur du risque change progressivement d'un polygone à l'autre. Le passage d'une zone à l'autre n'est donc pas bien représenté avec les modèles d’objets bien définis (crisp). Cette thèse propose des concepts fondamentaux pour le développement d'une approche combinant le paradigme GeoBI et le concept flou de considérer la présence de l’incertitude spatiale dans la représentation des zones à risque. En fin de compte, nous supposons cela devrait améliorer l’analyse du risque. Pour ce faire, un cadre conceptuel est développé pour créer un model conceptuel d’une base de donnée multidimensionnelle avec une application pour l’analyse du risque d’érosion côtier. Ensuite, une approche de la représentation des risques fondée sur la logique floue est développée pour traiter l'incertitude spatiale inhérente liée à l'imprécision et le flou des objets. Pour cela, les fonctions d'appartenance floues sont définies en basant sur l’indice de vulnérabilité qui est un composant important du risque. Au lieu de déterminer les limites bien définies entre les zones à risque, l'approche proposée permet une transition en douceur d'une zone à une autre. Les valeurs d'appartenance de plusieurs indicateurs sont ensuite agrégées basées sur la formule des risques et les règles SI-ALORS de la logique floue pour représenter les zones à risque. Ensuite, les éléments clés d'un cube de données spatiales floues sont formalisés en combinant la théorie des ensembles flous et le paradigme de GeoBI. En plus, certains opérateurs d'agrégation spatiale floue sont présentés. En résumé, la principale contribution de cette thèse se réfère de la combinaison de la théorie des ensembles flous et le paradigme de GeoBI. Cela permet l’extraction de connaissances plus compréhensibles et appropriées avec le raisonnement humain à partir de données spatiales et non-spatiales. Pour ce faire, un cadre conceptuel a été proposé sur la base de paradigme GéoBI afin de développer un cube de données spatiale floue dans le system de Spatial Online Analytical Processing (SOLAP) pour évaluer le risque de l'érosion côtière. Cela nécessite d'abord d'élaborer un cadre pour concevoir le modèle conceptuel basé sur les paramètres de risque, d'autre part, de mettre en œuvre l’objet spatial flou dans une base de données spatiales multidimensionnelle, puis l'agrégation des objets spatiaux flous pour envisager à la représentation multi-échelle des zones à risque. Pour valider l'approche proposée, elle est appliquée à la région Perce (Est du Québec, Canada) comme une étude de cas.Current Geospatial Business Intelligence (GeoBI) systems typically do not take into account the uncertainty related to vagueness and fuzziness of objects; they assume that the objects have well-defined and exact semantics, geometry, and temporality. Representation of fuzzy zones by polygons with well-defined boundaries is an example of such approximation. This thesis uses an application in Coastal Erosion Risk Analysis (CERA) to illustrate the problems. CERA polygons are created using aggregations of a set of spatial units defined by either the stakeholders’ interests or national census divisions. Despite spatiotemporal variation of the multiple criteria involved in estimating the extent of coastal erosion risk, each polygon typically has a unique value of risk attributed homogeneously across its spatial extent. In reality, risk value changes gradually within polygons and when going from one polygon to another. Therefore, the transition from one zone to another is not properly represented with crisp object models. The main objective of the present thesis is to develop a new approach combining GeoBI paradigm and fuzzy concept to consider the presence of the spatial uncertainty in the representation of risk zones. Ultimately, we assume this should improve coastal erosion risk assessment. To do so, a comprehensive GeoBI-based conceptual framework is developed with an application for Coastal Erosion Risk Assessment (CERA). Then, a fuzzy-based risk representation approach is developed to handle the inherent spatial uncertainty related to vagueness and fuzziness of objects. Fuzzy membership functions are defined by an expert-based vulnerability index. Instead of determining well-defined boundaries between risk zones, the proposed approach permits a smooth transition from one zone to another. The membership values of multiple indicators (e.g. slop and elevation of region under study, infrastructures, houses, hydrology network and so on) are then aggregated based on risk formula and Fuzzy IF-THEN rules to represent risk zones. Also, the key elements of a fuzzy spatial datacube are formally defined by combining fuzzy set theory and GeoBI paradigm. In this regard, some operators of fuzzy spatial aggregation are also formally defined. The main contribution of this study is combining fuzzy set theory and GeoBI. This makes spatial knowledge discovery more understandable with human reasoning and perception. Hence, an analytical conceptual framework was proposed based on GeoBI paradigm to develop a fuzzy spatial datacube within Spatial Online Analytical Processing (SOLAP) to assess coastal erosion risk. This necessitates developing a framework to design a conceptual model based on risk parameters, implementing fuzzy spatial objects in a spatial multi-dimensional database, and aggregating fuzzy spatial objects to deal with multi-scale representation of risk zones. To validate the proposed approach, it is applied to Perce region (Eastern Quebec, Canada) as a case study

Prototype system for supporting the incremental modelling of vague geometric configurations

In this paper the need for Intelligent Computer Aided Design (Int.CAD) to jointly support design and learning assistance is introduced. The paper focuses on presenting and exploring the possibility of realizing learning assistance in Int.CAD by introducing a new concept called Shared Learning. Shared Learning is proposed to empower CAD tools with more useful learning capabilities than that currently available and thereby provide a stronger interaction of learning between a designer and a computer. Controlled computational learning is proposed as a means whereby the Shared Learning concept can be realized. The viability of this new concept is explored by using a system called PERSPECT. PERSPECT is a preliminary numerical design tool aimed at supporting the effective utilization of numerical experiential knowledge in design. After a detailed discussion of PERSPECT's numerical design support, the paper presents the results of an evaluation that focuses on PERSPECT's implementation of controlled computational learning and ability to support a designer's need to learn. The paper then discusses PERSPECT's potential as a tool for supporting the Shared Learning concept by explaining how a designer and PERSPECT can jointly learn. There is still much work to be done before the full potential of Shared Learning can be realized. However, the authors do believe that the concept of Shared Learning may hold the key to truly empowering learning in Int.CAD

A Spatio-Temporal Framework for Managing Archeological Data

Space and time are two important characteristics of data in many domains. This is particularly true in the archaeological context where informa- tion concerning the discovery location of objects allows one to derive important relations between findings of a specific survey or even of different surveys, and time aspects extend from the excavation time, to the dating of archaeological objects. In recent years, several attempts have been performed to develop a spatio-temporal information system tailored for archaeological data. The first aim of this paper is to propose a model, called Star, for repre- senting spatio-temporal data in archaeology. In particular, since in this domain dates are often subjective, estimated and imprecise, Star has to incorporate such vague representation by using fuzzy dates and fuzzy relationships among them. Moreover, besides to the topological relations, another kind of spatial relations is particularly useful in archeology: the stratigraphic ones. There- fore, this paper defines a set of rules for deriving temporal knowledge from the topological and stratigraphic relations existing between two findings. Finally, considering the process through which objects are usually manually dated by archeologists, some existing automatic reasoning techniques may be success- fully applied to guide such process. For this purpose, the last contribution regards the translation of archaeological temporal data into a Fuzzy Temporal Constraint Network for checking the overall data consistency and reducing the vagueness of some dates based on their relationships with other ones

An Inexact Inferencing Strategy for Spatial Objects with Determined and Indeterminate Boundaries

For many years, spatial querying has been of interest for the researchers in the GIS community. Any successful implementation and long-term viability of the GIS technology depends on the issue of accuracy of spatial queries. In order to improve the accuracy and quality of spatial querying, the problems associated with the areas of fuzziness and uncertainty need to be addressed. There has been a strong demand to provide approaches that deal with inaccuracy and uncertainty in GIS. In this paper, we develop an approach that can perform fuzzy spatial querying under uncertainty. An inexact inferencing strategy for objects with determined and indeterminate boundaries is investigated, using type-2 fuzzy set theory