A Novel View of Bipolarity in Linguistic Data Summaries

The problem of data summarization of a set of (numeric) data, notably a (relational) database is dealt with. We are concerned with how to devise a short, (quasi) natural language summary, in the form of a sentence, which would best grasp the very content of the set of data. For instance, for a personnel database with records corresponding to particular employees who are described by attributes like age, sex, salary, etc., such a linguistic summary with respect to age may be “most employees are middle aged”. We use as a point of departure a fuzzy logic based approach to linguistic summarization originated by Yager, and then developed by Kacprzyk and Zadrożny who have also indicated—first—an intrinsic connection between linguistic summarization and fuzzy querying, and—second—a crucial role of protoforms in Zadeh’s sense. The second point of departure is the concept of a bipolar query in the sense that the querying criteria may be mandatory and optional, i.e. those which must be satisfied and those which should be satisfied if possible, as initiated by Zadrożny, and then developed by Zadrożny, Kacprzyk and De Tré. In this paper we present the concept of a bipolar linguistic summary that combines the very concepts of a linguistic summary with that of bipolarity in the above sense, and also an analogous relation between the linguistic summaries and bipolar queries.