Patrick Bosc

SQLf Query Functionality on Top of a Regular Relational Database Management System

This paper is mainly concerned with the extension of database management systems querying capabilities, so that users may address queries involving preferences and get discriminated answers. The use of flexible (gradual) predicates interpreted in the framework of the fuzzy set theory is advocated for defining a query language, called SQLf. This language enlarges the functionalities offered by SQL and it is considered here from a query processing point of view.

Fuzzy functional dependencies and redundancy elimination

In the context of regular relational databases, functional dependencies have received a lot of attention, since they capture some semantics about the data related to redundancy. Functional dependencies lead to an appropriate design of a database in terms of a set of relations and can make the checking process of integrity constraints significantly easier. For about 10 years, several proposals to deal with ill-known information in database management systems have been made, and extensions of the relational data model have been proposed accordingly. In this context, the idea of fuzzy functional dependency has emerged to extend the classical functional dependency, and several definitions have been proposed. In this article, an overview of these different proposals is provided, and the connection between fuzzy functional dependencies and database design is discussed. In addition, some semantics and use of fuzzy functional dependencies are suggested.

Value-Based and Representation-Based Querying of Possibilistic Databases

In this paper, we address the issue of querying imperfect data represented by possibility distributions. We distinguish between two types of queries: those involving conditions on the values, and those involving criteria on the representations of ill-known values. These two approaches are successively considered. We first recall some classical results relating to the querying of databases involving null values, and we point out the problems that arise in the specific context of disjunctive weighted data when value-based queries are dealt with. The necessity of defining a typology of relevant queries is emphasized. Then, we introduce a new querying framework allowing to handle ill-known data at a representation level. This framework, based on the notion of a weighted set, offers an alternative solution to the use of value-based queries and thus could be used to extend the querying capabilities of database systems aimed at handling ill-known values.

An Ordinal Approach to the Processing of Fuzzy Queries with Flexible Quantifiers

This paper studies queries to a database, involving expressions of the form ‘Q A-x’s are B’s’ where A and B are properties which may be fuzzy and with respect to which objects x’s are evaluated, and where Q is a quantifier which may stand for ‘all’, or may leave room for exceptions (‘at least q%’, ‘(at least) most’, etc.). An example of such a query is ‘Find the departments where most young employees are well-paid’. Such queries are discussed from a modeling and evaluation point of view, taking also into consideration what the user intends to ask when (s)he addresses this type of queries to a database system. Clarifying what has to be evaluated is specially important in the case where A is fuzzy, since then the boundaries of A are ill-defined and A may be somewhat empty.

On the comparison of aggregates over fuzzy sets

Publisher Summary This chapter deals with flexible queries addressed to regular relational databases where conditions are defined by fuzzy sets. A particular type of fuzzy conditions is investigated, where two aggregates applying to fuzzy sets are compared. The chapter proposes a sound interpretation for such statements in the context of flexible querying, that is, such that a degree of satisfaction is obtained. As a consequence, the set of answers returned to the user is discriminated from the best answers to less satisfactory ones. Many approaches to define flexible querying have been proposed in the last decades and it has been shown that fuzzy set theory provides a unifying framework to define flexible queries. In such a framework, fuzzy sets and a given condition lead to a degree of satisfaction. So far, conditions calling on aggregate functions (count, sum, max, min, and avg) were restricted to regular sets and this chapter examines the situation where aggregates may apply to fuzzy sets. In order to be coherent with the considered context, the interpretation of such a condition must be a unique degree of fulfillment.

Evaluation of flexible queries: the quantified statement case

Many propositions to extend database management systems have been made in the last decade. Some of them aim to support a wider range of queries involving fuzzy predicates expressing preferences and this paper focuses on the evaluation of a particular subset of queries, namely those using fuzzy quantified statements. More precisely, we consider the queries calling on a partitioning where a linguistic quantifier appears in the set-oriented condition. This condition is expressed by a quantified statement of type Q X are A and its degree of truth is assumed to be computed via the Sugeno fuzzy integral. This paper proposes algorithms to evaluate such queries and the main objective is to reduce processing time by saving data access. Heuristics are integrated into the algorithms in order to conclude on the result without accessing all elements of the referential.

23 – Fuzzy Theory Techniques and Applications in Data-Base Management Systems

Publisher Summary This chapter deals with the representation and the handling of ill-known values in relational databases. Database management systems are software components designed to store, retrieve, update, and control large amounts of permanent data. The chapter presents various frameworks for the modeling of imperfect data and focuses on the possibilistic framework, which proves to be the best suited to the representation of imprecise and/or uncertain information. After recalling the basic axioms and theorems of the possibilistic model, the chapter deals with two different ways of querying a database containing ill-known values represented as possibility distributions. The first one called “value-based querying,” uses a fuzzy pattern matching mechanism and allows for evaluating queries of the same kind as in the usual case. The second one is an alternative way of retrieving ill-known data, involving conditions on the representations of the data.

Vacuity-Oriented Generalized Yes/No Queries Addressed to Possibilistic Databases

In this chapter, extended relational databases are considered where some attribute values are imprecisely known. The need for imperfect data is more and more recognized and imprecise information can appear in diverse situations such as data warehouses, forecasts, incomplete archives, structured data extracted from texts, or systems where information issued from automated recognition procedures is stored. Different formalisms can be used to represent imprecise information (see [7] for instance), and the possibilistic setting is assumed in the rest of the chapter. A key question is to define a sound semantics for queries addressed to imprecise databases. Since imprecise data are represented as (possibly infinite) sets of acceptable candidates, an imprecise database can be seen as a set of regular databases, called worlds, associated with a choice for each attribute value. This approach provides a rational starting point for the definition of a query in the sense that its result is the set of the results obtained for each world (or interpretation). Unfortunately, such an approach is intractable, obviously in the case of an infinite number of worlds, but also due to the possibly huge number of worlds when it is finite. This observation leads to consider only specific queries which can be processed directly against the possibilistic database (the processing is then called “compact”), while delivering a result equivalent to the one defined in terms of worlds. The principle of the approach advocated is summarized in figure 1. A compact calculus valid for a subset of the relational algebra has been devised (see [4] for details). One of its characteristics is to deal with queries containing binary operations allowing for the composition of relations. In this context, the result of a query is a possibilistic relation whose interpretations correspond to more or less possible results, equivalent to those which would have been obtained with a calculus applied to worlds. This achievement is

An Approach Based on Predicate Correlation to the Reduction of Plethoric Answer Sets

Seeking data from large-scale databases often leads to a plethoric answer problem. A possible approach to reduce the set of retrieved items and to make it more manageable is to constrain the initial query with additional predicates. The approach presented in this paper relies on the identification of correlation links between predicates related to attributes of the relation of interest. Thus, the initial query is strengthened by additional predicates that are semantically close to the user-specified ones.

Non Monotonic Aggregates Applying to Fuzzy Sets in Flexible Querying

Abstract This paper considers flexible queries against relational databases using fuzzy set theory. More precisely, it is concerned with fuzzy conditions involving an aggregate operator (such as the maximum or the sum). In the general case, the interpretation of such conditions is not trivial since the aggregate applies to a fuzzy referential as in the condition “the average of high salaries is over