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Crisply Generated Complex Fuzzy Concepts Analysis Using Shannon Entropy

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Abstract

Recently, the properties of complex fuzzy concept lattice given a way to represent the uncertainty and its fluctuation. It given a well established mathematical model for understanding the dark data sets with respect to phase of time. The complex graphical structure visualization given a way to discover some of the useful pattern for decision making process. The problem arises when large number of complex fuzzy concepts are generated from the given context. To resolve this issue, a method is proposed for generating the complex fuzzy concepts based on maximal acceptance of complex fuzzy attributes (or objects) at given period of time. The information content is measured on Shannon entropy for the given phase of time. Thereafter, the complex fuzzy concepts are reduced based on their computed weight at different granulation to control the information pollution with an illustrative example. The obtained results are compared with recently available approaches on complex fuzzy concept lattice.

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Notes

  1. https://en.wikipedia.org/wiki/Dark_data

  2. https://en.wikipedia.org/wiki/Tide.

  3. https://en.wikipedia.org/wiki/Information_pollution.

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Acknowledgements

Author obliged for the time and suggestions given by reviewers and editor.

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  1. Department of Computer Science and Engineering, Gandhi Institute of Technology and Management–Visakhapatnam, Andhra Pradesh, 530045, India

    Prem Kumar Singh

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Appendix

Appendix

Nomenclature

Meaning

K

Formal fuzzy context

K

Complex fuzzy context

L

Scale of truth degree

X

Set of objects

\(x_i\)

i th–object

Y

Set of fuzzy attributes

\({\tilde{Y}}\)

Set of complex fuzzy attributes

\(y_j\)

j th–attribute

R

L–relation between X and R

\({\tilde{R}}\)

Complex fuzzy relation between X and R

r

Amplitude of complex fuzzy set in [0, 1]

\(\theta \)

Phase term of complex fuzzy set in \([0, \pi ]\)

P

Complex fuzzy Probability

Z

Complex fuzzy set

\(\mu _z\)

Membership–values of complex fuzzy element \(z \in Z\)

\(p_{i}\)

i th–Object Probability

(\(\uparrow , \downarrow \))

Galois connection

A

Extent

B

Intent

\(\bigcup \)

Union

\(\bigcap \)

Intersection

\(\wedge \)

Infimum

\(\vee \)

Supremum

\(\alpha \)

Granulation

E

Average information weight

\(\sum \)

Summation

m

Total number of complex fuzzy attributes

n

Total number of complex fuzzy objects

\(w_{j}\)

Weight of attribute

\(W_{j}\)

Weight of j–th concept

\(\textit{CFC}_\mathbf{{F} }\)

Set of complex fuzzy concepts

V

Vertex of complex fuzzy set

\(\mu _c\)

Complex membership of vertex

\(\rho _c\)

Complex membership of edges

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Singh, P.K. Crisply Generated Complex Fuzzy Concepts Analysis Using Shannon Entropy. Neural Process Lett 54, 5643–5667 (2022). https://doi.org/10.1007/s11063-022-10878-7

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