Hierarchical bipolar fuzzy queries: Towards more human consistent flexible queries

We are concerned with the so-called bipolar database queries which are meant here as those in which the query is composed of a necessary and optional part connected with a non-conventional aggregation operator “and possibly” as, for instance, in the query “find houses in a database of a real estate agency which are cheap and possibly close to a railroad station”. We first analyse some foundational issues related to the bivariate unipolar scales employed, and various interpretations of the “and possibly” aggregation operator. We concentrate on its logical representation via various connectives known in multivalued (fuzzy) logic. We propose a novel concept of a hierarchical bipolar database query in which, basically, the original query is considered a level 0 query at the bottom of the precisiation hierarchy, then its necessary and optional parts are assumed to be bipolar queries themselves. This makes it possible to further precisiate the user's intentions/preferences. A level 1 of precisiation is obtained, and the process is continued as far as it is necessary for the user to adequately reflect his/her intentions/preferences as to what is sought.