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Group-by is a core database operation that is used extensively in data analysis and decision support systems. In many application scenarios, it appears useful to group values according to their compliance with a certain concept instead of founding the grouping on value equality. In this paper, we propose a new SQLf construct that supports fuzzy-partition-based group-by (FGB). We show that FGB can be used to generate fuzzy summaries as well as to mine fuzzy association rules (whose head or body are bound to a specific fuzzy value) in a practical and efficient way. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in taking preferences into account for division-like queries. The interest for introducing preferences is first to cope with user needs, then to get discriminated results instead of a flat set of elements. Here, the idea is to use ordinal preferences which are not too demanding for a casual user. Moreover, the type of query considered is inspired by the division operator and some of its variations where preferences apply only to the divisor. The division aims at retrieving the elements associated with a specified set of values and in a similar spirit, the anti-division looks for elements which are associated with none of the values of a given set. One of the focuses of this paper is to investigate queries mixing those two aspects. In order to remain coherent with the denomination of (anti-)division, the property of the result delivered is characterized. Last, a special attention is paid to the implementation of such queries using a regular database management system and some experimental results illustrate the feasibility of the approach. [ABSTRACT FROM AUTHOR]

In this paper, we describe an approach to database preference queries based on the notion of outranking, suited to the case where partial preferences are incommensurable. This model constitutes an alternative to the use of Pareto order. Even though outranking does not define an order in the strict sense of the term, we describe a technique which yields a complete pre-order, based on a global aggregation of the outranking degrees computed for each pair of tuples. [ABSTRACT FROM AUTHOR]

Retrieving data from large-scale databases sometimes leads to plethoric answers especially when queries are under-specified. To overcome this problem, we propose to strengthen the initial query with additional predicates. These predicates are selected among predefined ones according principally to their degrees of semantic correlation with the initial query in order to avoid an excessive modification of its initial scope. According to the size of the initial answer set and the number of expected results specified by the user, fuzzy cardinalities are used to assess the reduction capability of these correlated predefined predicates. [ABSTRACT FROM AUTHOR]

This article presents an approach to database flexible queries which relies on the notion of outranking and a classification process. Instead of being compared pairwise like in Pareto-order-based approaches, tuples are compared to acceptability profiles that are associated with predefined classes. According to their satisfaction of user preferences, tuples are assigned to classes with a certain degree. This approach proposes a classification algorithm with a linear complexity and makes it possible to aggregate non-commensurable preferences. [ABSTRACT FROM AUTHOR]

This paper deals with the modeling and querying of a database containing uncertain attribute values, in the situation where some knowledge is available about the more or less certain value (or disjunction of values) that a given attribute in a given tuple can take. This is represented in the setting of possibility theory. A relational database model suited to this context is introduced, and selection, join and union operators of relational algebra are extended so as to handle such relations. It is shown that i) the model in question is a strong representation system for the algebraic operators considered, and that ii) the data complexity associated with the extended operators in this context is the same as in the classical database case, which makes the approach highly scalable. A possibilistic logic encoding of the model is also outlined. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in taking preferences into account for a family of queries inspired by the relational division. A division query aims at retrieving the elements associated with a specified set of values and usually the results remain not discriminated. So, we suggest the introduction of preferences inside such queries with the following specificities: i) the user gives his/her preferences in an ordinal way and ii) the preferences apply to the divisor which is defined as a hierarchy of sets. Different uses of the hierarchy are investigated, which leads to queries conveying different semantics and the property of the result in terms of a quotient is studied. A special attention is paid to the implementation of such queries using a regular database management system and some experimental results illustrate the feasibility of the approach. [ABSTRACT FROM AUTHOR]

This paper deals with the interpretation of database queries with preference conditions of the form ˵attribute is low (resp. medium, high)″ in the situation where the user is not aware of the actual content of the database but still wants to retrieve the best possible answers (relatively to that content). An approach to the definition of the terms ˵low″, ˵medium″ and ˵high″ in a contextual and relative manner is introduced. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in taking preferences into account for a family of queries inspired by the anti-division. An anti-division query aims at retrieving the elements associated with none of the elements of a specified set of values. We suggest the introduction of preferences inside such queries with the following specificities: i) the user gives his/her preferences in an ordinal way and ii) the preferences apply to the divisor which is defined as a hierarchy of sets. Different uses of the hierarchy are investigated, which leads to queries conveying different semantics and the property of the result delivered is characterized. [ABSTRACT FROM AUTHOR]

This paper investigates the use of fuzzy logic mechanisms coming from the database community, namely graded inclusions, to model the information retrieval process. In this framework, documents and queries are represented by fuzzy sets, which are paired with operations like fuzzy implications and T-norms. Through different experiments, it is shown that only some among the wide range of fuzzy operations are relevant for information retrieval. When appropriate settings are chosen, it is possible to mimic classical systems, thus yielding results rivaling those of state-of-the-art systems. These positive results validate the proposed approach, while negative ones give some insights on the properties needed by such a model. Moreover, this paper shows the added-value of this graded inclusion-based model, which gives new and theoretically grounded ways for a user to easily weight his query terms, to include negative information in his queries, or to expand them with related terms. [ABSTRACT FROM AUTHOR]

This chapter deals with the querying of possibilistic relational databases, by means of generalized yes/no queries whose form is: ˵to what extent is it possible and certain that the answer to Q satisfies property P″. Here, we consider cardinality-based generalized yes/no queries (in this case, property P is about cardinality) for which a processing technique is proposed, which avoids computing all the worlds attached to the possibilistic database. [ABSTRACT FROM AUTHOR]

In this paper, we present an algebraic relational operator called antidivision and we describe a range of interpretations that can be attached to this operator in the context of databases with fuzzy relations (i.e., relations that contain weighted tuples). We also study the way(s) this operator can be made tolerant to exceptions in order to limit the risk of obtaining empty answers. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an algebraic relational operator called antidivision and we describe a range of interpretations that can be attached to this operator in the context of databases with fuzzy relations (i.e., relations that contain weighted tuples). [ABSTRACT FROM AUTHOR]

One of the common problems that users are confronted with in their web data retrieval is overabundant answers, that is, being provided with an avalanche of responses that satisfy their queries. Most users are overwhelmed by such responses since it is difficult to examine them. In this paper, we attempt to address this issue in the context of flexible queries. The basic idea behind the solution proposed consists in modulating the fuzzy conditions involved in the user query by applying an appropriate transformation. This operation aims at intensifying the constraints of the query to make it more demanding. A transformation that relies on a convenient tolerance relation is introduced. The main features of our proposal are investigated as well. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper deals with the querying of possibilistic relational databases, by means of queries called generalized yes/no queries, whose general form is: "to what extent is it possible that the answer to Q satisfies property P". Here, property P concerns the inclusion in the result, of a set of tuples specified by the user. A processing technique for such queries is proposed, which avoids computing the worlds attached to the possibilistic database. [ABSTRACT FROM AUTHOR]

In this paper, we discuss an approach for relaxing a failing query in the context of flexible querying. The approach relies on the notion of proximity which is defined in a relative way. We show how such proximity allows for transforming a given predicate into an enlarged one. The resulting predicate is semantically not far from the original one and it is obtained by a simple fuzzy arithmetic operation. We show also how the search for a non-failing relaxed query over the lattice of relaxed queries can be improved by exploiting the notions of MFSs (Minimal Failing Sub-queries) and MGQs (Maximally Generalized failing Queries) of the original query. [ABSTRACT FROM AUTHOR]

In this paper, we present a cooperative approach for avoiding empty answers to fuzzy relational queries. We propose a relaxation mechanism generating more tolerant queries. This mechanism rests on a transformation that consists in applying a tolerance relation to fuzzy predicates contained in the query. A particular tolerance relation, which can be conveniently modeled in terms of a parameterized proximity relation, is discussed. The modified fuzzy predicate is obtained by a simple arithmetic operation on fuzzy numbers. We show that this proximity relation can be defined in a relative or in an absolute way. In each case, the main features of the resulting weakening mechanism are investigated. We also show that the limits of the transformation, that guarantee that the weakened query is not semantically too far from the original one, can be handled in a non-empirical rigorous way without requiring any additional information from the user. Lastly, to illustrate our proposal an example is considered. [ABSTRACT FROM AUTHOR]

Boolean queries may turn out to be too limited to answer certain users needs and it is desirable to envisage extended queries by introducing preferences in the conditions. In this paper, an extension of the division operator, called the approximate division, is studied where the operand relations are fuzzy ones (i.e., are made of weighted tuples) and the universal quantifier underlying the division is softened. The objective is twofold: i) to point out that fuzzy sets provide a convenient framework for the desired extension and ii) to show that the result of the approximate division is a quotient (in reference to the characterization of the quotient of two integers), which provides a well founded semantics. [ABSTRACT FROM AUTHOR]

In this paper, the issue of querying databases that may contain ill-known values represented by disjunctive weighted sets (possibility or probability distributions) is considered. The queries dealt with are of the form: "to what extent is it possible (or probable, depending on the framework considered) that tuple t belongs to the result of query Q", where Q denotes a usual relational query. In the possibilistic database framework, some previous works resulted in the definition of an evaluation method that does not entail computing the different possible worlds of the database. In this paper, we show that this method cannot be used in the probabilistic database framework in general. On the other hand, we describe an alternative evaluation method that is suitable for probabilistic queries when Q complies with certain constraints. [ABSTRACT FROM AUTHOR]

This paper deals with the querying of databases containing ill-known attribute values represented by possibility distributions. It investigates a query language with two operators: selection and a foreign key join operator which allows to express queries involving several relations at a time. The key idea is to impose a strong connection between the relations resulting from the operators and their interpretation in terms of more or less possible worlds. From a computational point of view, an interesting property of the queries considered is that they can be evaluated in a ˵compact″ way, i.e., they do not require explicit handling of the possible worlds attached to the possibilistic database. [ABSTRACT FROM AUTHOR]

With the increasing size of databases, the extraction of data summaries becomes more and more useful. The use of fuzzy sets seems interesting in order to extract linguistic summaries, i.e., statements from the natural language, containing gradual properties, which are meaningful for human operators. This paper focuses on the extraction from databases of linguistic summaries, using so-called fuzzy gradual rules, which encode statements of the form "the younger the employees, the smaller their bonus". The summaries considered here are more on the relations between labels of the attributes than on the data themselves. The first idea is to extract all the rules which are not in contradiction with tuples of a given relation. Then, the interest of these rules is questioned. For instance, some of them can reveal potential incoherence, while other are not really informative. It is then shown that in some cases, interesting information can be extracted from these rules. Last, some properties the final set of rules should verify are outlined. [ABSTRACT FROM AUTHOR]

The notion of flexible queries covers different meanings depending on the authors. Here, it is assumed to stand for queries involving preferences and the fuzzy set framework is advocated as a general tool for supporting the expression of preferences. If fuzzy queries can apply to regular databases where information stored is precisely known, one can wonder about the case where the database contains some ill-known data (represented as possibility distributions) and this issue is the heart of the paper. Two significantly different approaches are suggested. In the first one, any condition concerns the values themselves and its interpretation is based on a fuzzy pattern matching mechanism. Then, the answer of a query is uncertain, i.e., any element is associated with a possibility and a necessity degree. In the second approach, a condition relates to the representation of values, and, as such, returns a truth value which is certain. [ABSTRACT FROM AUTHOR]