Fuzzy-based Spatial Knowledge Discovery in Service of Efficient Coastal Erosion Risk Assessment

The need for effective spatial knowledge discovery in risk assessment increases as the amount of the spatial data which is handled and analyzed for risk assessment has enlarged. Such large variety of spatial data should be integrated from multiple sources presenting different types, semantics, and level of details weather geometrically, temporally, or thematically. Therefore, spatial knowledge discovery has been introduced to help decisions-makers with clear and efficient understanding of such complex cases of data integration. Risk, by itself, is a definition which is given to demonstrate the impact of a physical or human-induced phenomenon causing disasters or harming human-life. Spatial modeling and representing risk through risk zones (as crisp object) bring up the notion of the fiat nature of risk which is based on some interested criteria introduced by stakeholders and experts. In this regard, the issue of information vagueness appears in semantic definition of risk zones as well as geometries. Fiat nature of risk zones adds more complexity on risk assessment and risk zone representation as the conventional GIS methods and analytical information systems support such situations marginally. This paper presents the results of a PhD thesis in this regard entitled as “A Comprehensive Spatial Multidimensional Conceptual Model (SMCM) to Assess the Risk of Coastal Erosion Based on Fuzzy Set Theory”. To do so, the fuzzy spatial representation of risk zones and fuzzy multi-scale representation are dealt in order to improve risk assessment process and decision-making. Incorporating Geospatial Business Intelligence (GeoBI) paradigm and fuzzy set theory within Spatial Online Analytical Processing (SOLAP) necessitates developing a framework for designing key elements of a spatial datacube: dimensions, members, hierarchies, measures, and facts based on risk components (hazard, elements at risk and vulnerability). Thereafter, formalizing and adapting fuzzy model in such datacube should be carried out. Finally, some aggregation methods for fuzzy spatial data should be developed to deal with multiscale representation of risk zones as well as for navigating within such system (roll-up and drilldown operations). Background and Relevance Coastal Erosion Risk (CER) is a complex and dynamic process which is the result of several multi-scale and spatiotemporal interactions between hazard and vulnerability of the elements at risk (Alexander, 2000; Blaikie, Cannon, Davis, & Wisner, 2004; Daudé et al., 2009; Varnes, 1984). The inherent complexity of coastal erosion makes assessment of the associated risks complex as well (Cheng, Molenaar, & Stein, 2009). In fact, modeling the erosion, predicting its behavior over time, and estimating its impact on assets and human lives requires processing a large amount of heterogeneous data from multiple sources with different types and levels of details (Jadidi, Mostafavi, Bédard, Long, & Grenier, 2013). Therefore, an information system is required to accommodate and integrate the available heterogeneous data from different sources. This system should also provide users and decision makers with on-the-fly aggregation, analysis, synthesis, and reporting. Therefore, three main issues are conferenced in any Coastal Erosion Risk Assessment (CERA) for any selected region. The first issue is related to the huge amount of data with diverse semantics and from different sources. This introduces uncertainty and information vagueness right at the beginning of a risk assessment process (Bakillah, 2012; Sboui, 2010). The second issue is related to the distinct and multi-scale characteristics of risk based on the needs and interests of the participants and decision-makers (Jadidi, Mostafavi, Bédard, et al., 2013). This emphasizes the need for a risk-aware hierarchical data aggregation method in any CERA process (Cheng et al., 2009; Jadidi, Mostafavi, Bédard, et al., 2013). The third issue is that coastal risk zones have vague semantic definitions and are spatially or temporally uncertain as well as inherently multi-scale. The representation of such zones has been under intense investigations (Cheng et al., 2009; Dilo, By, & Stein, 2007). However, the literature introduces isolated solutions regarding exclusives issues. Indeed, an integrated approach covering all three under one umbrella (in case of CERA) is still missing. Probabilistic and Possibilistic approaches are the two main approaches which are widely employed to characterize information vagueness associated with risk modeling and representation (Aerts, Goodchild, & Heuvelink, 2003; Choa, Choi, & Kim, 2003; Cowell & Zeng, 2003; Darbra, Eljarrat, & Barceló, 2008; Fisher, Cheng, & Wood, 2007; Kentel & Aral, 2007). The flexibility of the possibilistic approaches such as fuzzy-based model for dealing with information vagueness suggests an efficient solution for spatial representation of risk (Kentel & Aral, 2007). Nevertheless, the idea of fuzzy spatial data model is still a young topic in the Geospatial Business Intelligence (GeoBI) communities. Few efforts have tried to embed the vagueness for spatiotemporal information in SOLAP (Bejaoui, 2009; Siqueira & Ciferri, 2012). But, these efforts are mainly based on extended spatial crisp models. Indeed, none of the cited works use Fuzzy Set Theory explicitly to characterize information vagueness and to integrate it in SOLAP in a systemic way. Moreover, the methods to aggregate spatial measures resulting from uncertain data (i.e. information vagueness) into multiple hierarchical dimensions (and to represent them) are still missing. Methods and Data To overcome the stated issues, this research has been carried out in three phases (see Figure 1): First, an analytical conceptual framework is proposed to develop a spatial multidimensional conceptual model (SMCM) for CERA. This framework includes four main steps including needs analysis, data inventory, definition of risk components (i.e. hazard, elements at risk, and associated vulnerability index), and finally designing a SMCM which includes identifying analysis dimensions and measures to calculate associated risk (Jadidi, Mostafavi, Bédard, et al., 2013). Second, Fuzzy Set Theory is selected to overcome the issue of information vagueness (Dilo, 2006; Kanjilal, Liu, & Schneider, 2010; Molenaar & Cheng, 2000; Pauly & Schneider, 2010; Robinson, 2003; Schneider, 2003a, 2003b). Our proposed approach for CERA is inspired from (Schneider, 2003b). A conceptual framework is then proposed based on Schneider’s model consisting of five main steps: (1) Identify hazard, (2) Elaborate vulnerability index, (3) Discretization (grid structures) , (4) Fuzzification, and (5) Fuzzy representation (Jadidi, Mostafavi, & Bédard, 2013). A MATLAB code is developed to perform Fuzzification and Fuzzy representation steps. A membership function is assigned to each cell while the risk value in each cell and for each indicator is assessed using the respective Fuzzy IF-THEN rules extracted from risk components. The membership functions serve to determine the level of risks. After calculating the risk for each indicator, the results are aggregated using an appropriate fuzzy operator (union, intersection, and difference) to calculate the overall risk. Third, the proposed fuzzy-based approach is then formalized and adapted for the SMCM which was proposed in phase I (Jadidi, Bédard, & Mostafavi, 2013). This necessitates identifying where the fuzziness happens and how this can be embedded into the database and managed while performing the queries and representing the results. In this regards, spatial datacube key elements (i.e. spatial level’s attributes, spatial levels, spatial members, spatial dimension, spatial hierarchy, spatial measures, and spatial facts) are redefined. Tow concepts of fuzzy partition (a grid-based cell) and fuzzy hierarchy relations are proposed to build such system. Overlay (union, intersection, difference), fusion, and some arithmetic operators are also planned and developed for such system for spatial aggregation purpose. Figure 1: A scheme of fuzzy based analytical conceptual approach proposed for CERA The region along the coast of the St-Laurence River in Percé, near the tip of the Gaspé Peninsula in Eastern Quebec, Canada is identified as a potential study site to implement and validate the proposed methods. Table 1 presents a list of the datasets and the related parameters that are used for CERA in this case study. Source Vulnerability Indicators ( i v ) LiDAR Data Slop , DEM, Erosion Rate Technical and Research Reports Protection structure, Infrastructure situation, Type of Coastline Google Open Street Map Analysis units Statistic Canada Population, density of population, economical values Quebec Prov. Transport Dept. Road network Table 1: Data sources and extracted coastal erosion risk parameters (vulnerability indicators), details are provided in (Jadidi, Mostafavi, Bédard, et al., 2013)