550 research outputs found
Characterizing One-Sided Formal Concept Analysis by Multi-Adjoint Concept Lattices
Managing and extracting information from databases is one of the main goals in several
fields, as in Formal Concept Analysis (FCA). One-sided concept lattices and multi-adjoint concept
lattices are two frameworks in FCA that have been developed in parallel. This paper shows that
one-sided concept lattices are particular cases of multi-adjoint concept lattices. As a first consequence
of this characterization, a new attribute reduction mechanism has been introduced in the one-side
framework.This research was partially supported by the 2014-2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in Project PID2019-108991GB-I00 and with the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia in Project FEDER-UCA18-108612 and by the European Cooperation in Science & Technology (COST) Action CA17124
On the Use of F-transform on the Reduction of Concept Lattices
In this paper, we show that F-transform can be used to re- duce relational databases. Subsequently, we show that the respective concept lattice is reduced significantly as well. Moreover, we present a clarifying example of the procedure.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.
The research was supported by the European Regional Development Fund by projects (CZ.1.05/1.1.00/02.0070) and (TIN12-39353- C04-04)
Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA
The detection of redundant or irrelevant variables (attributes) in datasets becomes essential in different frameworks, such as in Formal Concept Analysis (FCA). However, removing such variables can have some impact on the concept lattice, which is closely related to the algebraic structure of the obtained quotient set and their classes. This paper studies the algebraic structure of the induced equivalence classes and characterizes those classes that are convex sublattices of the original concept lattice. Particular attention is given to the reductions removing FCA's unnecessary attributes. The obtained results will be useful to other complementary reduction techniques, such as the recently introduced procedure based on local congruences
Interpretation of Fuzzy Attribute Subsets in Generalized One-Sided Concept Lattices
In this paper we describe possible interpretation and reduction of fuzzy attributes in Generalized One-sided Concept Lattices (GOSCL). This type of concept lattices represent generalization of Formal Concept Analysis (FCA) suitable for analysis of datatables with different types of attributes. FCA as well as generalized one-sided concept lattices represent conceptual data miningmethods. With growing number of attributes the interpretation of fuzzy subsets may become unclear, hence another interpretation of this fuzzy attribute subsets can be valuable. The originality of the presented method is based on the usage of one-sided concept lattices derived from submodels of former object-attribute model by grouping attributes with the same truth value structure. This leads to new method for attribute reduction in GOSCL environment
Impact of Local Congruences in Attribute Reduction
Local congruences are equivalence relations whose equivalence classes are convex sublattices of the original lattice. In this paper,
we present a study that relates local congruences to attribute reduction
in FCA. Specifically, we will analyze the impact in the context of the use
of local congruences, when they are used for complementing an attribute
reduction
Rough matroids based on coverings
The introduction of covering-based rough sets has made a substantial
contribution to the classical rough sets. However, many vital problems in rough
sets, including attribution reduction, are NP-hard and therefore the algorithms
for solving them are usually greedy. Matroid, as a generalization of linear
independence in vector spaces, it has a variety of applications in many fields
such as algorithm design and combinatorial optimization. An excellent
introduction to the topic of rough matroids is due to Zhu and Wang. On the
basis of their work, we study the rough matroids based on coverings in this
paper. First, we investigate some properties of the definable sets with respect
to a covering. Specifically, it is interesting that the set of all definable
sets with respect to a covering, equipped with the binary relation of inclusion
, constructs a lattice. Second, we propose the rough matroids based
on coverings, which are a generalization of the rough matroids based on
relations. Finally, some properties of rough matroids based on coverings are
explored. Moreover, an equivalent formulation of rough matroids based on
coverings is presented. These interesting and important results exhibit many
potential connections between rough sets and matroids.Comment: 15page
Distributed Computation of Generalized One-Sided Concept Lattices on Sparse Data Tables
In this paper we present the study on the usage of distributed version of the algorithm for generalized one-sided concept lattices (GOSCL), which provides a special case for fuzzy version of data analysis approach called formal concept analysis (FCA). The methods of this type create the conceptual model of the input data based on the theory of concept lattices and were successfully applied in several domains. GOSCL is able to create one-sided concept lattices for data tables with different attribute types processed as fuzzy sets. One of the problems with the creation of FCA-based models is their computational complexity. In order to reduce the computation times, we have designed the distributed version of the algorithm for GOSCL. The algorithm is able to work well especially for data where the number of newly generated concepts is reduced, i.e., for sparse input data tables which are often used in domains like text-mining and information retrieval. Therefore, we present the experimental results on sparse data tables in order to show the applicability of the algorithm on the generated data and the selected text-mining datasets
Rough sets based on Galois connections
Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of approximation operators are based on an indiscernibility relation, which is an equivalence one. Lately. different papers have motivated the possibility of considering arbitrary relations. Nevertheless, when those are taken into account, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution to the arising problems by presenting an alternative definition of approximation operators based on the closure and interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks
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