Factorization of matrices with grades via essential entries

Bělohlávek, Radim; Trnečková, Markéta

doi:10.1016/j.fss.2018.07.004

Cited by 8 publications

(2 citation statements)

References 7 publications

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“…Such a procedure is a generalization of the BFA which is a kind of an extension of the classic FA idea to categorical data. It can also be compared to the association relation in the HICLASS model for ordinal-scale variables, or to the similarity relationship analysis in the fuzzy context and fuzzy concept lattices developed by Belohlavek [39] and extended later by Belohlavek et al [40][41][42].…”

Section: Relation To Other Methodsmentioning

confidence: 99%

“…Formal concepts allow to restrict the solutions' search space and are generated by contextual knowledge about relationships between objects and attributes. In [41,42], the binary approach is generalized to fuzzy data and relationships, such that properties and theorems from formal concepts used in BFA apply also if attributes and relations are assessed by the truth value from multimodal logic, i.e., by values from the interval [0, 1]. Recent advances regarding formal concept analysis involving dimensionality reduction may also be found, for example, in [43,44].…”

Section: Background and Related Workmentioning

confidence: 99%

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Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

Grobelny

Michalski

Weber

2020

Neural Comput & Applic

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In this work, we propose a new method for modeling human reasoning about objects’ similarities. We assume that similarity depends on perceived intensities of objects’ attributes expressed by natural language expressions such as low, medium, and high. We show how to find the underlying structure of the matrix with intensities of objects’ similarities in the factor-analysis-like manner. The demonstrated approach is based on fuzzy logic and set theory principles, and it uses only maximum and minimum operators. Similarly to classic eigenvector decomposition, we aim at representing the initial linguistic ordinal-scale (LOS) matrix as a max–min product of other LOS matrix and its transpose. We call this reconstructing matrix a neuromatrix because we assume that such a process takes place at the neural level in our brain. We show and discuss on simple, illustrative examples, how the presented way of modeling grasps natural way of reasoning about similarities. The unique characteristics of our approach are treating smaller attribute intensities as less important in making decisions about similarities. This feature is consistent with how the human brain is functioning at a biological level. A neuron fires and passes information further only if input signals are strong enough. The proposal of the heuristic algorithm for finding the decomposition in practice is also introduced and applied to exemplary data from classic psychological studies on perceived similarities between colors and between nations. Finally, we perform a series of simulation experiments showing the effectiveness of the proposed heuristic.

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Section: Relation To Other Methodsmentioning

confidence: 99%

Section: Background and Related Workmentioning

confidence: 99%

Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

Grobelny

Michalski

Weber

2020

Neural Comput & Applic

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Study on the Necessity Operator to Factorize Formal Contexts in a Multi-adjoint Framework

Aragón

Medina

Ramírez‐Poussa

2022

Information Processing and Management of Uncertainty in Knowledge-Based Systems

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Factorizing formal contexts from closures of necessity operators

Aragón,

Medina,

Ramírez-Poussa

2024

Comp. Appl. Math.

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Factorizing datasets is an interesting process in a multitude of approaches, but many times it is not possible or efficient the computation of a factorization of the dataset. A method to obtain independent subcontexts of a formal context with Boolean data was proposed in Dubois and Prade based on the operators used in possibility theory. In this paper, we will analyze this method and study different properties related to the pairs of sets from which a factorization of a formal context arises. We also inspect how the properties given in the classical case can be extended to the fuzzy framework, which is essential to obtain a mechanism that allows the computation of independent subcontexts of a fuzzy context.

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Factorization of matrices with grades via essential entries

Cited by 8 publications

References 7 publications

Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

Study on the Necessity Operator to Factorize Formal Contexts in a Multi-adjoint Framework

Factorizing formal contexts from closures of necessity operators

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