Computing Implications with Negation from a Formal Context

Missaoui, Rokia; Nourine, Lhouari; Renaud, Yoan

doi:10.3233/fi-2012-659

Cited by 17 publications

(7 citation statements)

References 34 publications

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“…In 2012, Missaoui et.al. [3] have approached the generation of mixed implications from two given sets of implications only with positive and negative attributes respectively. We have followed this line: in [7], we extended the classical FCA framework with new derivation operators constituting a Galois connection for the treatment of negative and positive information in FCA and in [5,6] we proposed some mining algorithms to derive directly mixed implications.…”

Section: Summary Of the Workmentioning

confidence: 99%

Inference of Mixed Information in Formal Concept Analysis

Enciso

Mora

Rodríguez‐Jiménez

2018

Trends in Mathematics and Computational Intelligence

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Negative information can be considered twofold: by means of a negation operator or by capturing the absence of information. In this second approach, a new framework have to be developed: from the syntax to the semantics, including the management of such generalized knowledge representation. In this work we traverse all these issues in the framework of formal concept analysis, introducing a new set of inference rules to manage mixed (positive and negative) attributes.

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Section: Summary Of the Workmentioning

confidence: 99%

Inference of Mixed Information in Formal Concept Analysis

Enciso

Mora

Rodríguez‐Jiménez

2018

Trends in Mathematics and Computational Intelligence

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“…To approach the problem of obtaining a syntactic derivation system, R. Missaoui et al propose to add the following inference rules to Armstrong's axioms: for all

a, b \in M \cup \overset{M}{false}

and

A \subseteq M \cup \overset{M}{false}

,…”

Section: Negative Attributes and Mixed Conceptsmentioning

confidence: 99%

“…In this way, they provide a sound and complete syntactic system that allows to reason about m‐implications. Furthermore, in they also provide a method to mining m‐implications from a context based on the search of minimal sets of positive/negative attributes with 0 support (minimal keys). It is obvious that supp( A ) = 0 in a formal context when

Pos (A) \cap Neg (A) \neq \emptyset

and consequently, by [Cont],

A \to M \overset{M}{false}

holds.…”

Section: Negative Attributes and Mixed Conceptsmentioning

confidence: 99%

Data mining algorithms to compute mixed concepts with negative attributes: an application to breast cancer data analysis

Rodríguez‐Jiménez

Enciso

Mora

2016

Math Methods in App Sciences

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In the design of mathematical methods for a medical problem, one of the kernel issues is the identification of symptoms and measures that could help in the diagnosis. Discovering connections among them constitute a big challenge because it allows to reduce the number of parameters to be considered in the mathematical model. In this work, we focus on formal concept analysis as a very promising technique to address this problem. In previous works, we have studied the use of formal concept analysis to manage attribute implications. In this work, we propose to extend the knowledge that we can extract from every context using positive and negative information, which constitutes an open problem. Based on the main classical algorithms, we propose new methods to generate the lattice concept with positive and negative information to be used as a kind of map of attribute connections. We also compare them in an experiment built with datasets from the UCI repository for machine learning. We finally apply the mining techniques to extract the knowledge contained in a real data set containing information about patients suffering breast cancer. The result obtained have been contrasted with medical scientists to illustrate the benefits of our proposal.

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“…And 3WCA thinks over positive and negative information independently. A few works [12,18] have recently been served to rule acquisition or implications by integrating with negative information. Although Wei et al [25] studied rules acquisition of decision formal context based on three-way concept lattices, from which the rules are the forms of "If A, then C" and "If not B, then not D".…”

Section: Introductionmentioning

confidence: 99%

Rule reductions of decision formal context based on mixed information

Lin

2022

Appl Intell

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Three-way concept lattice extracts knowledge from positive and negative information separately. However, some applications require to mix positive and negative information for management and representation explicitly. In this paper, rule acquisition of FCA is extended based on mixed information. Firstly, two types of mixed concept lattices are studied. Then the relationships between mixed concept and classical concept, three-way concept are explored in depth. Secondly, mixed decision rules are investigated thoroughly. And the weak-basis is put forward to approximate to the basis of mixed decision rules. Finally, the comparison of mixed decision rules and three-way decision rules is perfectly discussed.

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Computing Implications with Negation from a Formal Context

Cited by 17 publications

References 34 publications

Inference of Mixed Information in Formal Concept Analysis

Inference of Mixed Information in Formal Concept Analysis

Data mining algorithms to compute mixed concepts with negative attributes: an application to breast cancer data analysis

Rule reductions of decision formal context based on mixed information

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