We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express stronger relationships between attribute values than the ordinary FDs. In our setting, the dependencies not only express that certain values are determined by others but also express that similar values of attributes imply similar values of other attributes. We show complete axiomatization using a system of Armstrong-like rules, comment on related computational issues, and the relational vs. propositional semantics of the dependencies. A logic for reasoning with similarity-preserving dependencies is proposed.Its semantics is defined using commutative integral partially ordered monoids.The logic is complete and decidable.A closure-like algorithm for non-contracting sets of dependencies is presented.Two kinds of semantics are discussed: a propositional and a relational one.
First, let us note that there exists a vast amount of papers on fuzzy functional dependencies'', often with questionable technical quality, which combine (in various ways) the concepts of fuzzy sets and functional dependencies in order to formalize vague dependencies between attributes. While this idea is tempting and close to what we present here, our objection is that most of these papers are purely definitional or just experimental and are not interested in the underlying logic in the narrow sense of it (i.e., in logic as a study of consequence). From one viewpoint this is not surprising since a number of papers in this category predate the beginning of systematic formalization of various types of fuzzy logics which appeared in the late 90's, see @cite_21 as a standard reference and a historical overview. One of the most influential early approaches that enjoyed interest in the database community is @cite_12 , further papers dealing with fuzzy functional dependencies and related phenomena include @cite_29 @cite_17 @cite_33 . Since our paper is not a survey, we do not write further details on such approaches and refer interested readers to @cite_39 where they can find further comments.
@cite_33 @cite_29 @cite_21 @cite_39 @cite_12 @cite_17
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This paper is situated in the area of fuzzy databases, i.e., databases containing imprecise information. More precisely, it deals with the notion of a functional dependency when data involved in this type of property are possibly imprecise. Contrary to previous works, the idea is not to fuzzify the concept of a functional dependency. In the view suggested here, we rather consider regular functional dependencies and we study the impact of the presence of such FDs on the insertion and handling of imprecise data. This paper deals with the application of fuzzy logic in a relational database environment with the objective of capturing more meaning of the data. It is shown that with suitable interpretations for the fuzzy membership functions, a fuzzy relational data model can be used to represent ambiguities in data values as well as impreciseness in the association among them. Relational operators for fuzzy relations have been studied, and applicability of fuzzy logic in capturing integrity constraints has been investigated. By introducing a fuzzy resemblance measure EQUAL for comparing domain values, the definition of classical functional dependency has been generalized to fuzzy functional dependency (ffd). The implication problem of ffds has been examined and a set of sound and complete inference axioms has been proposed. Next, the problem of lossless join decomposition of fuzzy relations for a given set of fuzzy functional dependencies is investigated. It is proved that with a suitable restriction on EQUAL, the design theory of a classical relational database with functional dependencies can be extended to fuzzy relations satisfying fuzzy functional dependencies. 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. Abstract The paper contains an analysis of integrity constraints for -ary relations in fuzzy databases. Apart from dependencies between all attributes there may be also dependencies describing relationships of fewer attributes. However, there is no complete arbitrariness. Relationships comprising ( 1) attributes must not infringe integrity constraints of the -ary relation. The analysis is carried out using the theory of functional dependencies. In this paper, we assume that attribute values are represented by means of interval-valued possibility distributions. The notion of fuzzy functional dependency has been appropriately extended according to the representation of fuzzy data. The paper formulates the rules to which fuzzy functional dependencies between ( 1) attributes of the -ary relation must be subordinated.