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Vague Entropy Measure for Complex Vague Soft Sets.

Ganeshsree Selvachandran1, Harish Garg2, Shio Gai Quek3

  • 1Department of Actuarial Science and Applied Statistics, Faculty of Business & Information Science, UCSI University, Jalan Menara Gading, Cheras 56000, Kuala Lumpur, Malaysia.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

The complex vague soft set (CVSS) model enhances data analysis for periodic phenomena by using complex-valued membership degrees. This approach improves handling of uncertainty, as demonstrated by new entropy measures and a robot image detection example.

Keywords:
complex fuzzy setcomplex vague soft setdistancedistance induced vague entropyvague entropy

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Area of Science:

  • Fuzzy Mathematics
  • Set Theory
  • Information Theory

Background:

  • Existing fuzzy set extensions handle uncertainty using real-number membership degrees.
  • Complex fuzzy sets and soft sets offer advanced modeling capabilities.
  • Periodic real-life phenomena present unique data representation challenges.

Purpose of the Study:

  • To introduce the complex vague soft set (CVSS) model, a hybrid of complex fuzzy and soft sets.
  • To develop novel entropy measures for the CVSS model based on distance axioms.
  • To investigate the properties and relations of these new entropy measures.

Main Methods:

  • Developed the CVSS model by relaxing membership degree constraints to complex unit disk subsets.
  • Defined new entropy measures for the CVSS model.
  • Axiomatically defined a distance measure to induce the entropy measures.
  • Investigated theoretical properties and interrelations of the proposed entropy measures.

Main Results:

  • The CVSS model effectively represents two-dimensional, periodic data.
  • New entropy measures for CVSS were successfully developed and their properties analyzed.
  • A numerical example demonstrated the practical application of the entropy measure in robot image detection.

Conclusions:

  • The CVSS model provides a more robust framework for handling uncertainty in complex data compared to traditional fuzzy sets.
  • The developed entropy measures offer a valuable tool for quantifying information and uncertainty within the CVSS environment.
  • The proposed methods show potential for applications in areas like image processing and pattern recognition.