A functional interpretation of linguistic summaries of data
This article concerns the definition of linguistic summaries of data in the relational model of databases. Among the different approaches, the propositions calling on linguistic quantifiers are very appealing since they offer flexibility and a linguistic formulation which can be easily understood by a user. More precisely, these linguistic summaries are made of a quantified statement associated with a degree of validity (computed from the database). Such a summary shows that a quantity of information (quantity described by the linguistic quantifier) satisfies a constraint (defined by a fuzzy predicate). This article shows that the already proposed approaches do not sufficiently stress the relationship between these two aspects. As a consequence, we propose another kind of linguistic summaries made of a linguistic statement associated with a degree of validity having a clear meaning in terms of quantity and quality. It becomes possible to compare two linguistic summaries and to understand the difference in their degrees of validity. These summaries are called functional linguistic summaries because their interpretation relies on a particular set-oriented function. They present the advantages of using fuzzy terms to reflect that the user does not exactly know what can be expected from the database. However, the degree of validity provides a precise description of the stored information. In other words, starting from a rough idea of what can be expected as a summary, the obtained degree of truth provides a precise description of the information stored in the database. The relationship of the proposed linguistic summaries with the quantified statements are studied in this paper. It turns out that these linguistic summaries can be viewed as particular quantified statements having particular properties.
linguistic summary linguistic quantifier fuzzy set