Within the framework of flexible querying of possibilistic databases, based on the fuzzy set theory, this chapter focuses on the case where the vocabulary used both in the querying language and in the data is hierarchically organized, which occurs in systems that use ontologies. We give an overview of previous works concerning two issues: first, flexible querying of imprecise data in the relational model and, second, the introduction of fuzziness in hierarchies. Concerning the latter point, we develop an aspect where there is a lack of study in current literature: fuzzy sets whose definition domains are hierarchies. Hence, we propose the concept of hierarchical fuzzy set and present its properties. We present its application in the MIEL flexible querying system for the querying of two imprecise relational databases, including user interfaces and experimental results.
Key Terms in this Chapter
Possibilistic Database: A database that contains ill-known data represented by means of the possibility theory.
Ontology: A formalization of the description of a domain knowledge at a conceptual level.
MIEL Language: A flexible querying language which permits expressing in a given view a conjunctive query. Current implementations have been done under Oracle and Postgresql RDBMS.
MIEL Query: A conjunctive query where the selection value associated with a queried attribute is expressed by a fuzzy set representing preferences.
Hierarchical Fuzzy Set: A fuzzy set whose definition domain is a part of a hierarchy.
Possibility Distribution: A fuzzy set whose semantics represents the possible ordered values of an imprecise datum; only one of these values is the effective—but ill-known—value of the datum.
Hierarchy: A set of elements that are partially ordered by the “kind of” relation.
Query Generalization: An operation that creates, from a given query Q1, a query Q2 such that Q1 is included in Q2; that is, the answers to Q1 are included in the answers to Q2 for any database.
Fuzzy Set: A mapping from a universe of discourse—definition domain of the fuzzy set—into the interval [0,1]. The concept of fuzzy set extends the notion of Boolean membership to a set to the notion of degree of membership.
Flexible Querying: Methods for querying a database that enhance standard querying expressiveness in various ways such as the expression of user’s preferences, query generalization, and so forth, in order to facilitate the extraction of relevant data.