56,269 research outputs found
Characterizing approximate-matching dependencies in formal concept analysis with pattern structures
Functional dependencies (FDs) provide valuable knowledge on the relations between attributes of a data table. A functional dependency holds when the values of an attribute can be determined by another. It has been shown that FDs can be expressed in terms of partitions of tuples that are in agreement w.r.t. the values taken by some subsets of attributes. To extend the use of FDs, several generalizations have been proposed. In this work, we study approximatematching dependencies that generalize FDs by relaxing the constraints on the attributes, i.e. agreement is based on a similarity relation rather than on equality. Such dependencies are attracting attention in the database field since they allow uncrisping the basic notion of FDs extending its application to many different fields, such as data quality, data mining, behavior analysis, data cleaning or data partition, among others. We show that these dependencies can be formalized in the framework of Formal Concept Analysis (FCA) using a previous formalization introduced for standard FDs. Our new results state that, starting from the conceptual structure of a pattern structure, and generalizing the notion of relation between tuples, approximate-matching dependencies can be characterized as implications in a pattern concept lattice. We finally show how to use basic FCA algorithms to construct a pattern concept lattice that entails these dependencies after a slight and tractable binarization of the original data.Postprint (author's final draft
Parameterizing the semantics of fuzzy attribute implications by systems of isotone Galois connections
We study the semantics of fuzzy if-then rules called fuzzy attribute
implications parameterized by systems of isotone Galois connections. The rules
express dependencies between fuzzy attributes in object-attribute incidence
data. The proposed parameterizations are general and include as special cases
the parameterizations by linguistic hedges used in earlier approaches. We
formalize the general parameterizations, propose bivalent and graded notions of
semantic entailment of fuzzy attribute implications, show their
characterization in terms of least models and complete axiomatization, and
provide characterization of bases of fuzzy attribute implications derived from
data
Characterization of order-like dependencies with formal concept analysis
Functional Dependencies (FDs) play a key role in many fields
of the relational database model, one of the most widely used database
systems. FDs have also been applied in data analysis, data quality, knowl-
edge discovery and the like, but in a very limited scope, because of their
fixed semantics. To overcome this limitation, many generalizations have
been defined to relax the crisp definition of FDs. FDs and a few of their
generalizations have been characterized with Formal Concept Analysis
which reveals itself to be an interesting unified framework for charac-
terizing dependencies, that is, understanding and computing them in a
formal way. In this paper, we extend this work by taking into account
order-like dependencies. Such dependencies, well defined in the database
field, consider an ordering on the domain of each attribute, and not sim-
ply an equality relation as with standard FDs.Peer ReviewedPostprint (published version
Extending FuzAtAnalyzer to approach the management of classical negation
FuzAtAnalyzer was conceived as a Java framework which goes beyond of classical tools in formal concept analysis. Specifically, it successfully incorporated the management of uncertainty by means of methods and tools from the area of fuzzy formal concept analysis. One limitation of formal concept analysis is that they only consider the presence of properties in the objects (positive attributes) as much in fuzzy as in crisp case.
In this paper, a first step in the incorporation of negations is presented. Our aim is the treatment of the absence of properties (negative attributes). Specifically, we extend the framework by including specific tools for mining knowledge combining crisp positive and negative attributes.Universidad de Málaga. Campus de Excelencia Internacional AndalucĂa Tech
Using concept lattices to mine functional dependencies
Concept Lattices have been proved to be a valuable tool to represent
the knowlegde in a database.
In this paper we show how functional dependencies in databases
can be extracted using Concept Lattices, not preprocessing the original
database,
but providing a new closure operator. We also prove that this method
generalizes the previous methods and
closure operators that are being used to find association rules in binary
databases.Postprint (published version
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