A context model for fuzzy concept analysis based upon modal logic

Huynh, Van–Nam; Nakamori, Yoshiteru; Ho, Tu Bao; Resconi, Germano

doi:10.1016/j.ins.2003.08.010

Cited by 11 publications

(5 citation statements)

References 33 publications

(49 reference statements)

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“…It means that other classes of fault-tolerant formal concepts might be more relevant than δ-bi-sets but also probably much harder to extract. Another related work in artificial intelligence concern the fuzzy concept analysis framework (see, e.g., [20]). It is an attempt to manage uncertainty and it is clearly related to noisy data analysis.…”

Section: Discussionmentioning

confidence: 99%

Towards Fault-Tolerant Formal Concept Analysis

Pensa

Boulicaut

2005

Lecture Notes in Computer Science

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Given Boolean data sets which record properties of objects, Formal Concept Analysis is a well-known approach for knowledge discovery. Recent application domains, e.g., for very large data sets, have motivated new algorithms which can perform constraint-based mining of formal concepts (i.e., closed sets on both dimensions which are associated by the Galois connection and satisfy some user-defined constraints). In this paper, we consider a major limit of these approaches when considering noisy data sets. This is indeed the case of Boolean gene expression data analysis where objects denote biological experiments and attributes denote gene expression properties. In this type of intrinsically noisy data, the Galois association is so strong that the number of extracted formal concepts explodes. We formalize the computation of the so-called δ-bisets as an alternative for capturing strong associations between sets of objects and sets of properties. Based on a previous work on approximate condensed representations of frequent sets by means of δ-free itemsets, we get an efficient technique which can be applied on large data sets. An experimental validation on both synthetic and real data is given. It confirms the added-value of our approach w.r.t. formal concept discovery, i.e., the extraction of smaller collections of relevant associations.

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Section: Discussionmentioning

confidence: 99%

Towards Fault-Tolerant Formal Concept Analysis

Pensa

Boulicaut

2005

Lecture Notes in Computer Science

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“…Looking at Fig. 10, we can see that the evaluation vectors from (1, 1, 1, 1, 1) to (5,5,5,5,5) lie on a single straight line. The small radii of the evaluation vectors (4, 4, 1, 4, 3) and (4,4,1,4,5) are attributable to the fact that they are nearly parallel with the eigenvector corresponding to the minimum eigenvector of D A .…”

Section: Evaluation Model Of Local Environment Based On Fuzzificationmentioning

confidence: 98%

“…[11]. Huynh et al [5] show that the context model [3] provides a practical framework for constructing membership functions of fuzzy concepts. This paper also tries to construct membership functions, but that express fuzziness of principal component scores, in a particular situation where we have to treat a set of subjective evaluation data.…”

Section: Introductionmentioning

confidence: 99%

Treating fuzziness in subjective evaluation data

Nakamori

Ryoke

2006

Information Sciences

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“…The mass assignment of a fuzzy concept is then considered as providing a probability based semantics for membership function of the fuzzy concept. A formal connection between this semantics of membership functions and the modal logic based interpretation of fuzzy concepts has been established in [10]. The mass assignment theory has been applied in some fields such as induction of decision trees [3], computing with words [12], among others.…”

Section: Fuzzy Setsmentioning

confidence: 99%