Rough-set-driven approach for attribute reduction in fuzzy formal concept analysis

Benítez-Caballero, M. José; Medina, Jesús; Ramírez‐Poussa, Eloísa; Ślęzak, Dominik

doi:10.1016/j.fss.2019.11.009

Cited by 37 publications

(14 citation statements)

References 40 publications

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“…Hence, this section analyzes the characterization when the set D does not contain unnecessary attributes. This study is interesting, for example, for any attribute reduction strategy merging FCA and other frameworks, such as rough set theory [35,42,43]. The first result shows that Statement 1 in Proposition 4 only arises when the context contains unnecessary attributes.…”

Section: Attribute Reduction Without Unnecessary Attributesmentioning

confidence: 90%

“…Moreover, Theorem 6 holds when the attribute reduction does not contain unnecessary attributes, as in FCA. If the reduction is given by another mechanism, such as based on the rough set theory philosophy [35,42,43], we can obtain classes that are not sublattices, as Example 3 shows. These facts also reinforce the necessity of studying mechanisms to lightly modify the equivalence relation given by the reduction in order to ensure that the classes are convex sublattices, as the new notion of local congruence [38,45] does.…”

Section: Attribute Reduction Without Unnecessary Attributesmentioning

confidence: 99%

“…The detection of (ir)relevant attributes or objects of a given formal context in FCA has been studied from different points of view, for example: in order to obtain a concept lattice isomorphic to the original one [22][23][24][25][26], to efficiently reduce the size of the concept lattice [8,[27][28][29][30][31][32], to extensional stability [33], to consider contexts with positive and negative attributes [34], to apply the rough set philosophy [35][36][37], etc. Notice that the different mechanisms focused on attribute reduction can dually be adapted to object reduction.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

2021

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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.

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Section: Attribute Reduction Without Unnecessary Attributesmentioning

confidence: 90%

Section: Attribute Reduction Without Unnecessary Attributesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

2021

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“…Due to the different evaluation purposes and requirements of WSN performance, it is difficult to establish a consistent indicator system. We design an indicator selection method based on the rough set theory to solve this problem [56,57]. It is assumed that a comprehensive evaluation indicator system containing two levels of indicators has been preliminarily established by referring to relevant literature.…”

Section: Indicator Selection Based On Rough Setmentioning

confidence: 99%

Research on the Evaluation Model for Wireless Sensor Network Performance Based on Mixed Multiattribute Decision‐Making

et al. 2021

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Many application fields initiate using wireless sensor network (WSN), and the evaluation for its performance becomes an important topic, which can help the decision-maker to find the deficiency of the current WSN or seek the best WSN. There exist mixed multiple attributes in the WSN performance evaluation process, for example, some evaluation indicators can be expressed as interval numbers, while others can be expressed as linguistic variables, so it is necessary to explore the evaluation model based on mixed multiattribute decision-making (MADM). Considering the specific evaluation purpose and requirements for different enterprises, this paper puts forward an indicator selection method and a subjective weighting method based on the rough set theory. After that, based on the transformation of mixed attributes into the unified intuitionistic fuzzy numbers (IFNs), an objective weighting method based on intuitionistic fuzzy entropy is proposed. Meanwhile, the combined weights of indicators are obtained by synthesizing the subjective and objective weights. Subsequently, in order to evaluate WSN performance objectively, an integrated comprehensive evaluation framework is proposed, which includes single evaluation, compatibility test, combination evaluation, and consistency test. The paper gives specific models and calculation steps in detail. Finally, it provides a case study to explain the application of the proposed indicator selection method and the evaluation models, which provide new ideas and references for WSN performance evaluation.

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“…In this paper we focus on the reduction of objects for a classification task. This kind of reduction has been seldom considered by the research community, which has mainly focused on attribute reduction [2,5,12,18]. Some examples of the study of object reductions are [15], which analyses the reduction of objects oriented to keep the original attribute reducts and [1,13,16,22,23] that reducts objects and attributes in parallel.…”

Section: Introductionmentioning

confidence: 99%

Representative Set of Objects in Rough Sets Based on Galois Connections

Madrid

Ramírez‐Poussa

2020

Lecture Notes in Computer Science

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This paper introduces a novel definition, called representative set of objects of a decision class, in the framework of decision systems based on rough sets. The idea behind such a notion is to consider subsets of objects that characterize the different classes given by a decision system. Besides the formal definition of representative set of objects of a decision class, we present different mathematical properties of such sets and a relationship with classification tasks based on rough sets.

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Rough-set-driven approach for attribute reduction in fuzzy formal concept analysis

Cited by 37 publications

References 40 publications

Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

Research on the Evaluation Model for Wireless Sensor Network Performance Based on Mixed Multiattribute Decision‐Making

Representative Set of Objects in Rough Sets Based on Galois Connections

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