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.     

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.     

Semantic measure of fuzzy data in extended possibility‐based fuzzy relational databases

In this paper, we propose notions of equivalence and inclusion of fuzzy data in relational databases for measuring their semantic relationship. The fuzziness of data appears in attribute values in forms of possibility distribution as well as resemblance relations in attribute domain elements. An approach for evaluating semantic measures is presented. With the proposal, one can remove fuzzy data redundancy and define fuzzy functional dependency. © 2000 John Wiley & Sons, Inc.     

Ordered functional dependencies in relational databases

We extend the relational data model to incorporate linear orderings into data domains, which we call the ordered relational model. The conventional Functional Dependencies (FDs) are examined in the context of ordered relational databases by using the notion of System Ordering Independence (SOI), which refers to the desirable scenario that the ordering of tuples in a relation is independent of the implementation of the underlying DBMS. We also extend Armstrong's axiom system for FDs to object relations, which are a subclass of ordered relations that allow us to view tuples as objects. We formally define Ordered Functional Dependencies (OFDs) for the extended model by means of two possible extensions of domains, pointwise-orderings and lexicographical orderings. We first present a sound and complete axiom system for OFDs in the case of pointwise-orderings and then establish a sound and complete set of chase rules for OFDs in the case of lexicographical orderings. Our main result shows that the implication problems for both cases of OFDs are decidable, and that it is linear time for the case of pointwise-orderings.     

Normalization and lossless join decomposition of similarity‐based fuzzy relational databases

Fuzzy relational database models generalize the classical relational database model by allowing uncertain and imprecise information to be represented and manipulated. In this article, we introduce fuzzy extensions of the normal forms for the similarity‐based fuzzy relational database model. Within this framework of fuzzy data representation, similarity, conformance of tuples, the concept of fuzzy functional dependencies, and partial fuzzy functional dependencies are utilized to define the fuzzy key notion, transitive closures, and the fuzzy normal forms. Algorithms for dependency preserving and lossless join decompositions of fuzzy relations are also given. We include examples to show how normalization, dependency preserving, and lossless join decomposition based on the fuzzy functional dependencies of fuzzy relation are done and applied to some real‐life applications. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 885–917, 2004.     

Discovering functional and inclusion dependencies in relational databases

We consider the problem of discovering the functional and inclusion dependencies that a given database instance satisfies. This technique is used in a database design tool that uses example databases to give feedback to the designer. If the examples show deficiencies in the design, the designer can directly modify the examples. the tool then infers new dependencies and the database schema can be modified, if necessary. the discovery of the functional and inclusion dependencies can also be used in analyzing an existing database. the problem of inferring functional dependencies has several connections to other topics in knowledge discovery and machine learning. In this article we discuss the use of examples in the design of databases, and give an overview of the complexity results and algorithms that have been developed for this problem. © 1992 John Wiley & Sons, Inc.     

Appropriate inferences of data dependencies in relational databases

We study inference systems for the combined class of functional and full hierarchical dependencies in relational databases. Two notions of implication are considered: the original notion in which a dependency is implied by a given set of dependencies and the underlying set of attributes, and the alternative notion in which a dependency is implied by a given set of dependencies alone. The first main result establishes a finite axiomatisation for the original notion of implication which clarifies the role of the complementation rule in the combined setting. In fact, we identify inference systems that are appropriate in the following sense: full hierarchical dependencies can be inferred without use of the complementation rule at all or with a single application of the complementation rule at the final step of the inference only; and functional dependencies can be inferred without any application of the complementation rule. The second main result establishes a finite axiomatisation for the alternative notion of implication. We further show how inferences of full hierarchical dependencies can be simulated by inferences of multivalued dependencies, and vice versa. This enables us to apply both of our main results to the combined class of functional and multivalued dependencies. Furthermore, we establish a novel axiomatisation for the class of non-trivial functional dependencies.     

Unacceptable components in fuzzy relational databases

The existence of unacceptable components, which consist of unacceptable tuples and elements in attribute values, is shown in fuzzy relational databases. The unacceptable components are created by update operations, insertion, deletion, and modification. An unacceptable tuple in a relation is a tuple such that the degree of its not belonging to that relation is greater than that of its belonging to. The unacceptable tuple can be easily eliminated from relations. There are three kinds of unacceptable elements. One case of unacceptable elements is a redundant element created by insertion and modification. Another is an element created by a possible tuple value not at all or partially satisfying integrity constraints in insertion and modification. The other is an element created by a possible tuple value completely or partially satisfying update conditions in deletion. The unacceptable elements can be eliminated from relations without loss of information. As a result, we can obtain fuzzy relational databases without unacceptable components by a reasonable way. © 1996 John Wiley & Sons, Inc.     

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.     

Querying fuzzy relational databases through fuzzy domain calculus

In this paper we present a definition of a domain relational calculus for fuzzy relational databases using the GEFRED model as a starting point. It is possible to define an equivalent fuzzy tuple relational calculus and consequently we achieve the two query language levels that Codd designed for relational databases but these are extended to fuzzy relational databases: Fuzzy relational algebra (defined in the GEFRED model) and the fuzzy relational calculus which is put forward in this paper. The expressive power of this fuzzy relational calculus is demonstrated through the use of a method to translate any algebraic expression into an equivalent expression in fuzzy domain relational calculus. Furthermore, we include a useful system so that the degree to which each value has satisfied the query condition can be measured. Some examples are also included in order to clarify the definition. ©1999 John Wiley & Sons, Inc.     

Reasoning of fuzzy relational databases with fuzzy ontologies

A significant interest developed regarding the problem of describing databases with expressive knowledge representation techniques in recent years, so that database reasoning may be handled intelligently. Therefore, it is possible and meaningful to investigate how to reason on fuzzy relational databases (FRDBs) with fuzzy ontologies. In this paper, we first propose a formal approach and an automated tool for constructing fuzzy ontologies from FRDBs, and then we study how to reason on FRDBs with constructed fuzzy ontologies. First, we give their respective formal definitions of FRDBs and fuzzy Web Ontology Language (OWL) ontologies. On the basis of this, we propose a formal approach that can directly transform an FRDB (including its schema and data information) into a fuzzy OWL ontology (consisting of the fuzzy ontology structure and instance). Furthermore, following the proposed approach, we implement a prototype construction tool called FRDB2FOnto. Finally, based on the constructed fuzzy OWL ontologies, we investigate how to reason on FRDBs (e.g., consistency, satisfiability, subsumption, and redundancy) through the reasoning mechanism of fuzzy OWL ontologies, so that the reasoning of FRDBs may be done automatically by means of the existing fuzzy ontology reasoner.© 2012 Wiley Periodicals, Inc.     

Fuzzy relations and fuzzy relational databases

This paper deals with the connections existing between fuzzy set theory and fuzzy relational databases. Our new result dealing with fuzzy relations is how to calculate the greatest lower bound (glb) of two similarity relations. Our main contributions in fuzzy relational databases are establishing from fuzzy set theory what a fuzzy relational database should be (the result is both surprising and elegant), and making fuzzy relational databases even more robust.Our work in fuzzy relations and in fuzzy databases had led us into other interesting problems—two of which we mention in this paper. The first is primarily mathematical, and the second provides yet another connection between fuzzy set theory and artificial intelligence. In understanding similarity relations in terms of other fuzzy relations and in making fuzzy databases more robust, we work with closure and interior operators; we present some important properties of these operators. In establishing the connection between fuzzy set theory and artificial intelligence, we show that an abstraction on a set is in fact a partition on the set; that is, an abstraction defines an equivalence relation on the underlying set.     

An extended authorization model for relational databases

We propose two extensions to the authorization model for relational databases defined originally by P.G. Griffiths and B. Wade (1976). The first extension concerns a new type of revoke operation, called noncascading revoke operation. The original model contains a single, cascading revoke operation, meaning that when a privilege is revoked from a user, a recursive revocation takes place that deletes all authorizations granted by this user that do not have other supporting authorizations. The new type of revocation avoids the recursive revocation of authorizations. The second extension concerns negative authorization which permits specification of explicit denial for a user to access an object under a particular mode. We also address the management of views and groups with respect to the proposed extensions     

A note on approximation measures for multi-valued dependencies in relational databases

We consider the problem of defining a normalized approximation measure for multi-valued dependencies in relational database theory. An approximation measure is a function mapping relation instances to real numbers. The number to which an instance is mapped, intuitively, describes the strength of the dependency in that instance. A normalized approximation measure for functional dependencies has been proposed previously: the minimum number of tuples that need be removed for the functional dependency to hold divided by the total number of tuples. This leads naturally to a normalized measure for multi-valued dependencies: the minimum number of tuples that need be removed for the multi-valued dependency to hold divided by the total number of tuples.The measure for functional dependencies can be computed efficiently, O(|r|log(|r|)) where |r| is the relation instance. However, we show that an efficient algorithm for computing the analogous measure for multi-valued dependencies is not likely to exist. A polynomial time algorithm for computing the measure would lead to a polynomial time algorithm for an NP-complete problem (proven by a reduction from the maximum edge biclique problem in graph theory). Hence, we argue that it is not a good measure. We propose an alternate measure based on the lossless join characterization of multi-valued dependencies. This measure is efficiently computable, O(|r|²).     

An algebraic theory of functional and multivalued dependencies in relational databases

Computation of the dependency basis is the fundamental step in solving the membership problem for functional dependencies (FDs) and multivalued dependencies (MVDs) in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of a dependency-lattice and develop an algebraic characterization of inference basis using simple notions from lattice theory. We also establish several interesting properties of dependency-lattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a): computing the inference basis of a given set M of MVDs; (b): computing the dependency basis of a given attribute set w.r.t. M; and (c): solving the membership problem for MVDs. We also show that our results naturally extend to incorporate FDs also in a way that enables the solution of the membership problem for both FDs and MVDs put together. We finally show that our algorithms are more efficient than existing ones, when used to solve what we term the ‘generalized membership problem’.     

A logic approach to fuzzy relational databases

A new definition of Fuzzy Relational Database is given by using logical concepts. With this definition it is possible to consider several kinds of fuzziness for the database attributes. A Domain Calculus-based query language is also established for the model. It allows us to formulate several types of queries with different lack of precision levels. © 1994 John Wiley & Sons, Inc.     

A new definition of fuzzy functional dependency in fuzzy relational databases

The need to incorporate and treat information given in fuzzy terms in Relational Databases has concentrated a great effort in the last years. This article focuses on the treatment of functional dependencies (f.d.) between attributes of a relation scheme. We review other approaches to this problem and present some of its missfunctions concerning intuitive properties a fuzzy extension of f.d. should verify. Then we introduce a fuzzy extension of this concept to overcome the previous anomalous behaviors and study its properties. of primary interest is the completeness of our fuzzy version of Armstrong axioms in order to derive all the fuzzy functional dependencies logically implied by a set of f.f.d. just using these axioms. © 1994 John Wiley & Sons, Inc.     

Rule‐based approach for topic maps learning from relational databases

Relational databases (RDBs) have been widely used as back end for information systems. Considering that RDBs have valuable knowledge interwoven in between stored data, how to access, represent and share this knowledge becomes an important challenge. Topic maps (TMs) emerge as a good solution for this problem. However, manual development of TMs is a difficult, time‐consuming and subjective task if there is no common guideline. The existing TMs building approaches mainly consider the meta‐information contained in a RDB, without considering the knowledge residing in the database content (its current state). Other approaches require a predefined configuration for applying a specific data transformation. This paper proposes an automatic method for TM construction based on learning rules. Our method considers the background knowledge of the RDBs during the building process and was implemented and applied on a representative set of 15 RDBs. The resulting TMs were validated syntactically using a standard tool and validated semantically through the inference of information using a formal query language. In addition, an analysis between the relational data (input) and its representation (output) was conducted. The results found in our experiments are encouraging and put in evidence the soundness of the proposed method.     

The integrity constraints for similarity-based fuzzy relational databases

This paper first introduces a new definition for the conformance of tuples existing in a similarity-based fuzzy database relation. Then the formal definitions of fuzzy functional and multivalued dependencies are given on the basis of the conformance values presented here. These dependencies are defined to represent relationships between domains of the same relation that exist. The definitions of the fuzzy dependencies presented in this study allow a sound and complete set of inference rules. In this paper, we include examples to demonstrate how the integrity constraints imposed by these dependencies are enforced whenever a tuple is to be inserted or to be modified in a fuzzy database relation. © 1998 John Wiley & Sons, Inc.