\section{Conclusions and Future Work}
\label{sec:conclusion}

In this article, we propose \name, a novel abstract data type to handle vague spatial objects in the PostgreSQL with the PostGIS spatial extension. \name\ empowers the management of spatial applications by offering textual and binary representations for vague spatial objects and by providing an expressive set of spatial operations, including vague geometric set operations, vague topological predicates, vague numerical operations, and type-dependent vague spatial operations. As facilities, \name\ introduces SQL operators to handle results of vague topological predicates and vague numerical operations. We also introduce \nameimp, an improvement to \name\ to speed up the performance of spatial queries to process vague topological predicates.

Comparisons of \name\ with current functionalities available on PostgreSQL showed that \name\ provided better performance results for spatial queries with vague topological predicates. The performance gain of \name\ varied from 21\% up to 58\%. Empowered with \nameimp, \name\ provided even better results, which varied from 72\% up to 98\%. Future work will deal with the extension of \name\ to allow the use of index structures and the storage of statistical data about vague spatial objects to be used by the PostgreSQL query optimizer. 