Generalization of strategies for fuzzy query translation in classical relational databases

Users of information systems would like to express flexible queries over the data possibly retrieving imperfect items when the perfect ones, which exactly match the selection conditions, are not available. Most commercial DBMSs are still based on the SQL for querying. Therefore, providing some flexibility to SQL can help users to improve their interaction with the systems without requiring them to learn a completely novel language. Based on the fuzzy set theory and the α-cut operation of fuzzy number, this paper presents the generic fuzzy queries against classical relational databases and develops the translation of the fuzzy queries. The generic fuzzy queries mean that the query condition consists of complex fuzzy terms as the operands and complex fuzzy relations as the operators in a fuzzy query. With different thresholds that the user chooses for the fuzzy query, the user’s fuzzy queries can be translated into precise queries for classical relational databases.     

About quotient and division of crisp and fuzzy relations

The role and properties of the division are very well known in the context of queries addressed to regular relational databases. However, Boolean queries whose result is expressed in terms of all or nothing may turn out to be too limited to answer certain user needs and it is desirable to envisage extended queries by introducing preferences in the conditions. In this paper, two lines of extension of the division operator are studied: (i) operand relations of the division are fuzzy relations (i.e., they are made of weighted tuples) and (ii) the universal quantifier underlying the division is weakened. Various approaches to these extensions can be considered and one of our goals is to point out those which ensure that the resulting relation is a quotient (in reference to the characterization of the quotient of two integers). So doing, a sound semantics for the extended division is guaranteed.     

Generalizing database relational algebra for the treatment of incomplete or uncertain information and vague queries

This paper deals with relational databases which are extended in the sense that fuzzily known values are allowed for attributes. Precise as well as partial (imprecise, uncertain) knowledge concerning the value of the attributes are represented by means of [0,1]-valued possibility distributions in Zadeh's sense. Thus, we have to manipulate ordinary relations on Cartesian products of sets of fuzzy subsets rather than fuzzy relations. Besides, vague queries whose contents are also represented by possibility distributions can be taken into account. The basic operations of relational algebra, union, intersection, Cartesian product, projection, and selection are extended in order to deal with partial information and vague queries. Approximate equalities and inequalities modeled by fuzzy relations can also be taken into account in the selection operation. Then, the main features of a query language based on the extended relational algebra are presented. An illustrative example is provided. This approach, which enables a very general treatment of relational databases with fuzzy attribute values, makes an extensive use of dual possibility and necessity measures.     

Fuzzy query translation for relational database systems

The paper presents a new method for fuzzy query translation based on the alpha-cuts operations of fuzzy numbers. This proposed method allows the retrieval conditions of SQL queries to be described by fuzzy terms represented by fuzzy numbers. It emphasizes friendliness and flexibility for inexperienced users. The authors have implemented a fuzzy query translator to translate user's fuzzy queries into precise queries for relational database systems. Because the proposed method allows the user to construct his fuzzy queries intuitively and to choose different retrieval threshold values for fuzzy query translation, the existing relational database systems will be more friendly and more flexible to the users.     

关系数据库中基于EPTV的模糊查询

关系数据库中空值存在不同的语义,并且会影响模糊查询结果。针对该问题,提出用标号来区分空值的语义,并且在EPTV逻辑的基础上,对关系运算和一些复杂的嵌套查询进行扩展,给出相关定义和计算方法。通过实例说明,与常规模糊查询相比,该方法能较好地反映空值对模糊查询结果的影响。     

Algebraic equivalences of nested relational operators

Algebraic optimisation is both theoretically and practically important for query processing in complex value databases. In this paper, we consider this issue and investigate some algebraic properties concerning the nested relational operators.The join operation is one of the most time-consuming operations in nested relational query processing. We introduce a new join operator, called P-join, which combines the advantages of Roth's extended natural join and Colby's recursive join for efficient data access. We also investigate some algebraic properties concerning the P-join operator and extended relational operators, which can be used for query optimisation in nested relational databases.We then examine the role of the restructuring operators nest and unnest in their interactions with the extended relational operators proposed by Roth et al. Under certain functional and mutual data dependencies, the six nested relational equations will hold.Finally, we outline the steps of a heuristic optimisation algorithm that utilises algebraic transformation rules developed in this paper and previous related work to transform an initial query to an optimised one that is more efficient to execute.     

A NEW METHOD FOR FUZZY QUERY PROCESSING IN RELATIONAL DATABASE SYSTEMS

In this paper, we present a new method for fuzzy query processing in relational database systems based on automatic clustering techniques and weighting concepts. The proposed method allows the query conditions and the weights of query items of users' fuzzy SQL queries to be described by linguistic terms represented by fuzzy numbers. Because the proposed fuzzy query processing method allows the users to construct their fuzzy queries more conveniently, the existing relational database systems will be more intelligent and more flexible to the users.     

基于Vague关系数据模型的除操作研究

基于Vague集理论的Vague关系数据库由于其所含信息的模糊性,对应于现实世界的多种状态。为此,基于扩展的Vague关系数据模型,研究一种条件受限的Vague除操作实现方法,并给出相应的操作步骤和算法。实例分析结果表明,该实现方法可直接作用于整个Vague关系数据库,无需对Vague关系数据库对应的所有状态逐一进行扫描即可获得正确的操作结果,具有较高的执行效率。     

Rewriting rules to permeate complex similarity and fuzzy queries within a relational database system

In recent years, the availability of complex data repositories (e.g., multimedia, genomic, semistructured databases) has paved the way to new potentials as to data querying. In this scenario, similarity and fuzzy techniques have proven to be successful principles for effective data retrieval. However, most proposals are domain specific and lack of a general and integrated approach to deal with generalized complex queries, i.e., queries where multiple conditions are expressed, possibly on complex as well as on traditional data. To overcome such limitations, much work has been devoted to the development of middleware systems to support query processing on multiple repositories. On a similar line, We present a formal framework to permeate complex similarity and fuzzy queries within a relational database system. As an example, we focus on multimedia data, which is represented in an integrated view with common database data. We have designed an application layer that relies on an algebraic query language, extended with MM-tailored operators, and that maps complex similarity and fuzzy queries to standard SQL statements that can be processed by a relational database system, exploiting standard facilities of modern extensible RDBMS. To show the applicability of our proposal, we implemented a prototype that provides the user with rich query capabilities, ranging from traditional database queries to complex queries gathering a mixture of Boolean, similarity, and fuzzy predicates on the data.     

Efficient processing of nested Fuzzy SQL queries in a fuzzydatabase

In a fuzzy relational database where a relation is a fuzzy set of tuples and ill-known data are represented by possibility distributions, nested fuzzy queries can be expressed in the Fuzzy SQL language. Although it provides a very convenient way for users to express complex queries, a nested fuzzy query may be very inefficient to process with the naive evaluation method based on its semantics. In conventional databases, nested queries are unnested to improve the efficiency of their evaluation. In this paper, we extend the unnesting techniques to process several types of nested fuzzy queries. An extended merge-join is used to evaluate the unnested fuzzy queries. As shown by both theoretical analysis and experimental results, the unnesting techniques with the extended merge-join significantly improve the performance of evaluating nested fuzzy queries     

关系数据库中带语言值权重的模糊查询

在模糊理论的基础上,提出了将权重概念引入数据库模糊查询中,使用户对查询中各个属性的相对重视程度得以体现。为每条记录提供了一个匹配度,按匹配度的降序输出结果,方便用户选择。权重和匹配度都是语言变量［7］,其取值为语言值形式,更加贴近自然。     

An evidential reasoning approach to attribute value conflictresolution in database integration

Resolving domain incompatibility among independently developed databases often involves uncertain information. DeMichiel (1989) showed that uncertain information can be generated by the mapping of conflicting attributes to a common domain, based on some domain knowledge. We show that uncertain information can also arise when the database integration process requires information not directly represented in the component databases, but can be obtained through some summary of data. We therefore propose an extended relational model based on Dempster-Shafer theory of evidence to incorporate such uncertain knowledge about the source databases. The extended relation uses evidence sets to represent uncertainty in information, which allow probabilities to be attached to subsets of possible domain values. We also develop a full set of extended relational operations over the extended relations. In particular, an extended union operation has been formalized to combine two extended relations using Dempster's rule of combination. The closure and boundedness properties of our proposed extended operations are formulated. We also illustrate the use of extended operations by some query examples     

Domain-independent queries on databases with external functions

We study queries over databases with external functions, from a language-independent perspective. The input and output types of the external functions can be atomic values, flat relations, nested relations, etc. We propose a new notion of data-independence for queries on databases with external functions, which extends naturally the notion of generic queries on relational databases without external functions. In contrast to previous such notions, ours can also be applied to queries expressed in query languages with iterations. Next, we propose two natural notions of computability for queries over databases with external functions, and prove that they are equivalent, under reasonable assumptions. Thus, our definition of computability is robust. Finally, based on this equivalence result, we give examples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines (Abiteboul and V. Vianu, 1991; Abiteboul et al., 1992) are complete on nested relations: they are known not to be complete on flat relations.     

Updating extended possibility‐based fuzzy relational databases

Two kinds of fuzziness in attribute values of the fuzzy relational databases can be distinguished: one is that attribute values are possibility distributions and the other is that there are resemblance relations in attribute domains. The fuzzy relational databases containing these two kinds of fuzziness simultaneously are called extended possibility‐based fuzzy relational databases. In this article, we focus on such fuzzy relational databases and investigate three update operations for the fuzzy relational databases, which are Insertion, Deletion, and Modification, respectively. We develop the strategies and implementation algorithms of these operations. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 237–258, 2007.     

Deriving Object Oriented Federated Databases and Processing Federated Queries

In this paper, we present a federated query processing approach to evaluate queries on an Object-Oriented (OO) federated database. This approach has been designed and implemented in the OO-Myriad project, which is an OO extension to the Myriad FDBS researchmyriad:94. Since data integration is performed as part of federated query processing, we have proposed outerjoin, outer-difference and generalized attribute derivation operations together with the traditional relational operations, to be used for integration purposes. To define an OO federated database as a virtual view on multiple OO export databases, we adopt a database mapping strategy that systematically derives each of the class extents, deep class extents and relationships of the federated database using an operator tree consisting of the integration operations. By augmenting federated database queries with this algebraic mapping information, query execution plans can be generated. Based on the original Myriad query processing framework, we have realized the proposed OO federated query processing approach in the OO-Myriad prototype.     

Vague数据库Skyline查询技术研究

Skyline查询处理是近年来数据库领域的一个热门研究方向。由于现实世界中普遍存在着大量不精确、不确定的信息,Skyline查询也随之成为模糊数据处理中的一个重要内容。在已有研究的基础上,讨论了基于Vague关系数据模型的Skyline查询,其用于查询给定Vague关系中的任意元组确定不被该关系中的任意其它元组所支配的程度,并给出了相关的计算公式和查询算法,该算法可直接作用于Vague关系数据库,而无需对Vague关系数据库对应的所有可能性状态逐一进行扫描,具有较高的执行效率。在此基础上,还进一步讨论了带有预选择条件的Skyline查询的计算方法。     

基于关系数据库的模糊查询技术

在关系数据库中,SQL只能处理精确查询,而现实中存在许多模糊查询的问题。在模糊逻辑理论的基础上,提出了关系数据库的模糊查询思路,并详细地讨论了在数值和字符属性上的实现方法。实现方法不仅对数据库的查询进行了扩展,而且对实际系统的开发也有一定的借鉴作用。     

Handling fuzzy information in extended possibility‐based fuzzy relational databases

Two kinds of fuzziness in attribute values of the fuzzy relational databases can be distinguished: One is that attribute values are possibility distributions, and the other is that there are resemblance relations in attribute domains. The fuzzy relational databases containing these two kinds of fuzziness simultaneously are called extended possibility‐based fuzzy relational databases. In this paper, we focus on such fuzzy relational databases. We classify two kinds of fuzzy data redundancies and define their removal. On this basis, we define fuzzy relational operations in relational algebra, which, being similar to the conventional relational databases, are complete and sound. In particular, we investigate fuzzy querying strategies and give the form of fuzzy querying with SQL. © 2002 Wiley Periodicals, Inc.