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Top1. Introduction
In Bédard and Han (2009), Spatial On-Line Analytical Processing (SOLAP) is defined as a “Visual platform built especially to support rapid and easy spatiotemporal analysis and exploration of data following a multidimensional approach comprised of aggregation levels”. In this type of systems, cartographic, tabular and chart displays are used to interactively visualize and explore the data. The data are stored in a Spatial Data Warehouse (SDW) as a datacube that is the multidimensional model implementation (Salehi, Bédard, & Rivest, 2010). The decision-makers who use SOLAP tools are rarely fully aware of the spatial data uncertainty. Spatial data are usually represented by crisp objects in information systems, while, in fact it is often impossible to exactly know the spatial object boundaries. Thus, a clear gap is created between the majority of real world phenomena and their formal representation in spatial data warehouses (Cheng, Molenaar, & Lin, 2001). The SOLAP end-users are then exposed to erroneous analysis due to the uncertainty issues on data sources.
As indicated in Edoh-Alove, Bimonte, and Bédard (2014), only some recent research introduces spatial vagueness in the multidimensional model (Jadidi, Mostafavi, Bédard, & Long, 2012; Siqueira, Ciferri, Times, & Ciferri, 2014) and SOLAP operators to reduce the analysis errors. While Jadidi et al. (2012) have proposed an approach based on Fuzzy Set Theory and Tessellation to address spatial vagueness in SOLAP datacubes, and experimented it in coastal erosion management, Siqueira et al. (2014) have extended the multidimensional model to exploit vague objects exact models (Bejaoui, 2009; Pauly & Schneider, 2010) in SOLAP systems.
In Edoh-Alove et al. (2014), we proposed a design process where a risk-management approach was adopted to better deal with the spatial vagueness issues. This method was motivated by the need of sticking with existing SOLAP technologies which support vector-based cartographic dimensions implementation. The method, called Risk-Aware Design of SOLAP datacube (RADSOLAP) method, considers the risks of misinterpretation induced by vague data in the SOLAP datacubes and identified by spatial data experts and end-users. It also considers the tolerance levels of end-users to those risks, and based on those parameters, proposes to end-users a set of SOLAP datacube prototypes iteratively tailored to their tolerance levels. This paper goes beyond the work presented in Edoh-Alove et al. (2014) by proposing formal tools to support the key steps of the process. More specifically, we extended an existing UML Profile intended for SOLAP datacube modeling to take into account vague, risk and tolerance elements and we described and formalized the SOLAP datacubes prototypes tailoring to end-users tolerance levels in the forms of multidimensional schemas transformation functions and a transformation process.
In Section 2 of this paper, we briefly describe our RADSOLAP method alongside with the ICSOLAP UML Profile we have extended; in Section 3, an agricultural case study used to illustrate our proposals is presented; then in section 4, we detailed our new RADSOLAP UML profile and in section 5 the SOLAP datacube transformation process and functions; section 6 present the related work and finally, Section 6 concludes the paper.