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In this paper we propose extension of PostGIS Spatial Database Management system by imprecise point object type. Position imprecision is modelled as fuzzy point in R2 linear fuzzy space. The linear fuzzy space is defined over R2 where the membership function is convex, upper semi continuous, symmetric w.r.t core, linearly decreasing w.r.t core distance, and core is single point. The fuzzy convex hull is defined in the linear fuzzy space. Main functions that support operations between fuzzy points are implemented in Pl/PgSQL  language.