On a new type of contextual queries and linguistic summaries of a bipolar type

A new type of linguistic summaries, so-called contextual linguistic summaries, are further developed. The point of departure are contextual bipolar queries which play the same role for a new type of summaries as flexible fuzzy queries do with respect to the classical linguistic summaries. The bipolar queries employed are of a special type, following the required/desired semantics formalized using the “and possibly” operator and a recently introduced “or, if impossible” operator. The latter is inspired by the work of Lietard et al. on another bipolarity related operator “or else”. The “or, if impossible” operator is its non truth functional counterpart, interpreted in the same vein as the “and possibly” operator employed and studied in our previous work. In the paper we extend the concept of contextual linguistic summaries using this new operator and study its basic properties as well as some more general properties of this class of summaries.