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Bipolar-valued hesitant fuzzy graph and its application.

Sakshi Dev Pandey¹, A S Ranadive¹, Sovan Samanta²

¹Department of Mathematics, Guru Ghasidas Vishwavidyalya Bilaspur, Chhattisgarh, India.

Social Network Analysis and Mining

|December 7, 2021

Summary

This study introduces bipolar-valued hesitant fuzzy graphs (BVHFGs) to identify influential individuals in networks. The novel approach enhances existing fuzzy graph models by incorporating hesitation and bipolarity for more accurate social network analysis.

Keywords:

Bipolar-valued hesitant fuzzy graph Bipolar-valued hesitant fuzzy sets Directed bipolar-valued hesitant fuzzy graph Domination degree

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Area of Science:

Graph Theory
Social Network Analysis
Fuzzy Set Theory

Background:

Identifying influential individuals is crucial in social networks, conferences, and group discussions.
Fuzzy graphs (FGs) are effective tools for analyzing network influence.
Existing models may not fully capture the nuances of influence due to limitations in representing membership degrees.

Purpose of the Study:

To introduce and define the concept of bipolar-valued hesitant fuzzy graphs (BVHFGs).
To generalize hesitant fuzzy graphs (HFGs) by incorporating bipolar-valued hesitant fuzzy sets (BVHFs).
To develop a numerical method for identifying the most dominating person in a network using BVHFGs.

Main Methods:

Definition of BVHFGs using BVHF membership grades.
Exploration of basic operations and functional properties of BVHFGs.
Proposal of a numerical method for ranking individuals based on domination degrees.

Main Results:

BVHFGs offer a broader scope for representing imprecise membership grades compared to bipolar fuzzy graphs (BFGs).
The proposed numerical method considers both hesitation and bipolarity, providing an advantage over previous methods.
Application of the method to an example demonstrates significant changes in the ranking of dominating persons compared to HFGs and BVHFGs.

Conclusions:

BVHFGs provide a more comprehensive framework for social network analysis, especially for identifying influential members.
The developed numerical method offers a superior approach to ranking individuals by accounting for complex membership characteristics.
This research advances the application of fuzzy graph theory in real-world influence identification problems.