On three classes of division queries involving ordinal preferences

In this paper, we are interested in taking preferences into account for a family of queries inspired by the relational division. A division query aims at retrieving the elements associated with a specified set of values and usually the results remain not discriminated. So, we suggest the introduction of preferences inside such queries with the following specificities: (i) the user gives his/her preferences in an ordinal way and (ii) the preferences apply to the divisor which is defined as a hierarchy of sets. Different uses of the hierarchy are investigated, which leads to queries conveying different semantics and the property of the result in terms of a quotient is studied. Special attention is paid to the implementation of such extended division queries using a regular database management system along which some experiments to support the feasibility of the approach. Moreover, the issue of empty or overabundant answers is dealt with.