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Published on: July 24, 2016
Bipolar intuitionistic fuzzy graph based decision-making model to identify flood vulnerable region
Deva Nithyanandham1, Felix Augustin1, Samayan Narayanamoorthy2
1Mathematics Division, School of Advanced Sciences, Vellore Institute of Technology (Chennai Campus), Chennai, Tamil Nadu, India.
This study introduces covering, matching, and domination concepts for bipolar intuitionistic fuzzy graphs (BIFG). A BIFG model identifies flood-vulnerable zones in Chennai, highlighting Kodambakkam as the most susceptible area.
Area of Science:
- Graph Theory
- Fuzzy Mathematics
- Decision Science
Background:
- Traditional graph theory struggles with uncertain data.
- Bipolar intuitionistic fuzzy graphs (BIFG) extend fuzzy graphs for imprecise information.
- Covering, matching, and domination are key graph concepts needing adaptation for uncertainty.
Purpose of the Study:
- To define covering, matching, and domination concepts within BIFG framework.
- To develop novel approaches for these concepts when effective edges are absent.
- To apply BIFG for decision-making in real-world problems like disaster management.
Main Methods:
- Definition of covering, matching, and domination on BIFG using effective edges.
- Development of new methodologies for BIFG concepts without effective edges.
- Construction of a BIFG-based decision-making model for vulnerability assessment.
Main Results:
- Established definitions and theorems for covering, matching, and domination in BIFG.
- Successfully applied the BIFG model to identify flood-vulnerable zones in Chennai.
- Kodambakkam identified as the most susceptible zone based on the BIFG model.
- Demonstrated the model's efficiency through comparative analysis.
Conclusions:
- BIFG provides a robust framework for graph problems with uncertainty.
- The proposed BIFG model effectively identifies critical areas in disaster management.
- The study validates the superiority of the BIFG approach over existing methods.
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