Degree based models of granular computing under fuzzy indiscernibility relations

Muhammad Akram; Ahmad N. Al-Kenani; Anam Luqman; Muhammad Akram; Ahmad N. Al-Kenani; Anam Luqman

doi:10.3934/mbe.2021417

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 6: 8415-8443. doi: 10.3934/mbe.2021417

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Research article Special Issues

Degree based models of granular computing under fuzzy indiscernibility relations

1.
Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
2.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia

Academic Editor: Antonello Rizzi

Received: 29 July 2021 Accepted: 23 September 2021 Published: 27 September 2021

The aim of this research work is to put forward fuzzy models of granular computing based on fuzzy relation and fuzzy indiscernibility relation. Thanks to fuzzy information granulation to provide multi-level visualization of problems that include uncertain information. In such a granulation, fuzzy sets and fuzzy graphs help us to represent relationships among granules, groups or clusters. We consider the fuzzy indiscernibility relation of a fuzzy knowledge representation system ($ \mathcal{I} $). We describe the granular structures of $ \mathcal{I} $, including discernibility, core, reduct and essentiality of $ \mathcal{I} $. Then we examine the contribution of these structures to granular computing. Moreover, we introduce certain granular structures using fuzzy graph models and discuss degree based model of fuzzy granular structures. Granulation of network models based on fuzzy information effectively handles real life data which possesses uncertainty and vagueness. Finally, certain algorithms of proposed models are developed and implemented to solve real life problems involving uncertain granularities. We also present a concise comparison of the models developed in our work with other existing methodologies.
- fuzzy knowledge representation system,
- granular structures,
- fuzzy graphs,
- degree based models,
- comparative analysis
Citation: Muhammad Akram, Ahmad N. Al-Kenani, Anam Luqman. Degree based models of granular computing under fuzzy indiscernibility relations[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 8415-8443. doi: 10.3934/mbe.2021417

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Abstract

The aim of this research work is to put forward fuzzy models of granular computing based on fuzzy relation and fuzzy indiscernibility relation. Thanks to fuzzy information granulation to provide multi-level visualization of problems that include uncertain information. In such a granulation, fuzzy sets and fuzzy graphs help us to represent relationships among granules, groups or clusters. We consider the fuzzy indiscernibility relation of a fuzzy knowledge representation system ($ \mathcal{I} $). We describe the granular structures of $ \mathcal{I} $, including discernibility, core, reduct and essentiality of $ \mathcal{I} $. Then we examine the contribution of these structures to granular computing. Moreover, we introduce certain granular structures using fuzzy graph models and discuss degree based model of fuzzy granular structures. Granulation of network models based on fuzzy information effectively handles real life data which possesses uncertainty and vagueness. Finally, certain algorithms of proposed models are developed and implemented to solve real life problems involving uncertain granularities. We also present a concise comparison of the models developed in our work with other existing methodologies.

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