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Degree based models of granular computing under fuzzy indiscernibility relations.

Muhammad Akram1, Ahmad N Al-Kenani2, Anam Luqman1

  • 1Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan.

Mathematical Biosciences and Engineering : MBE
|November 24, 2021
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Summary

This study introduces fuzzy models for granular computing, using fuzzy relations and information granulation to visualize complex, uncertain data. The developed algorithms effectively handle real-world problems with vague information.

Keywords:
comparative analysisdegree based modelsfuzzy graphsfuzzy knowledge representation systemgranular structures

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Area of Science:

  • Computer Science
  • Information Science
  • Artificial Intelligence

Background:

  • Fuzzy information granulation offers multi-level visualization for uncertain data.
  • Fuzzy sets and graphs are used to represent relationships within data granules.
  • Fuzzy knowledge representation systems are foundational for granular computing.

Purpose of the Study:

  • To propose fuzzy models for granular computing based on fuzzy relation and fuzzy indiscernibility relation.
  • To describe and examine granular structures within fuzzy knowledge representation systems.
  • To develop and implement algorithms for real-life problems involving uncertain granularities.

Main Methods:

  • Utilizing fuzzy relation and fuzzy indiscernibility relation for granular computing models.
  • Employing fuzzy sets and fuzzy graphs to model relationships among data granules.
  • Developing and implementing algorithms based on fuzzy granular structures and network models.

Main Results:

  • Description and analysis of granular structures including discernibility, core, reduct, and essentiality.
  • Introduction of fuzzy graph models and degree-based models for fuzzy granular structures.
  • Successful implementation of algorithms to solve real-life problems with uncertain granularities.

Conclusions:

  • The proposed fuzzy models effectively handle uncertainty and vagueness in real-life data granulation.
  • Fuzzy granular computing provides a robust framework for visualizing and analyzing complex information.
  • The developed methodologies offer a valuable contribution to the field of granular computing and data analysis.