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Concept Learning Using Vague Concept Lattice

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Abstract

Recently, the theory of Formal Concept Analysis is extensively studied with bipolar fuzzy setting for adequate analysis of vagueness in fuzzy attributes via a defined sharp boundary. However, many real life data sets contain vague attributes (i.e. beautiful, bald, and tadpole) which cannot be defined through a sharp or restricted boundaries. To process these types of data sets the current paper focused on disparate representation of vagueness in attributes through its evidence to support and reject. To achieve this goal, a method is proposed to generate vague concept lattice with an illustrative example.

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Abbreviations

\(t_{A}\) :

Truth membership value

\(f_{A}\) :

False membership value

F :

Formal fuzzy context

(X, Y, \(\tilde{R}\)):

Formal fuzzy context-F

X :

Set of objects

Y :

Set of attributes

L :

Scale of truth degree

L :

Residuated lattice

\(\tilde{R}\) :

A map from \(X \times Y\) to L

\(\otimes \) :

Multiplication

\(\rightarrow \) :

Residuum

a, b, c :

Elements in L

(\(\uparrow , \downarrow \)):

Galois connection

A :

Extent

B :

Intent

\(L^{{\textit{X}}}\) :

L-set of objects

\(L^{{\textit{Y}}}\) :

L-set of attributes

\(\bigcup \) :

Union

\(\bigcap \) :

Intersection

\(\wedge \) :

Infimum

\(\vee \) :

Supremum

m :

Total number of attributes

n :

Total number of objects

\(\textit{FC}_\mathbf{F }\) :

Set of concepts

I, J, Z :

Non-empty vague set

V :

Vertex set

\(v_{1}, v_{2}, v_{3}\) :

Vertex of graph

\(\rho \) :

Edges of fuzzy graph

T :

Fuzzy graph

\(v_{1}v_{2}, v_{2}v_{3}, v_{3}v_{1}\) :

Edges in the vague graph

E :

Vague set of edges

G :

Vague graph

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Acknowledgements

Author is thankful to all the referees and editor for their valuable suggestions and comments.

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Authors and Affiliations

  1. Amity Institute of Information Technology, Amity University, Sector-125, Noida, Uttar Pradesh, 201313, India

    Prem Kumar Singh

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  1. Prem Kumar Singh
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Correspondence to Prem Kumar Singh.

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Singh, P.K. Concept Learning Using Vague Concept Lattice. Neural Process Lett 48, 31–52 (2018). https://doi.org/10.1007/s11063-017-9699-y

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