Newly defined fuzzy Misbalance Prodeg Index with application in multi-criteria decision-making

Shama Liaqat; Zeeshan Saleem Mufti; Yilun Shang; Shama Liaqat; Zeeshan Saleem Mufti; Yilun Shang

doi:10.3934/math.2024984

AIMS Mathematics

2024, Volume 9, Issue 8: 20193-20220. doi: 10.3934/math.2024984

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Research article

Newly defined fuzzy Misbalance Prodeg Index with application in multi-criteria decision-making

1.
Department of Mathematics and Statistics, The University of Lahore, Lahore Campus, Pakistan
2.
Department of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne, UK

Received: 22 March 2024 Revised: 23 May 2024 Accepted: 05 June 2024 Published: 21 June 2024
MSC : 05C15

In crisp graph theory, there are numerous topological indices accessible, including the Misbalance Prodeg Index, which is one of the most well-known degree-based topological indexes. In crisp graphs, both vertices and edges have membership values of $ 1 $ or $ 0 $, whereas in fuzzy graphs, both vertices and edges have different memberships. This is an entire contrast to the crisp graph. In this paper, we introduce the Fuzzy Misbalance Prodeg Index of a fuzzy graph, which is a generalized form of the Misbalance Prodeg Index of a graph. We find bounds of this index and find bounds of certain classes of graphs such as path graph, cycle graph, complete graph, complete bipartite graph, and star graph. We give an algorithm to find the Fuzzy Misbalance Prodeg Index of a graph for the model of multi-criteria decision-making is established. We present applications from daily life in multi-criteria decision-making. We apply our obtained model of the Fuzzy Misbalance Prodeg Index for the multi-criteria decision-making to the choice of the best supplier and we also show the graphical analysis of our index with the other indices that show how our index is better than other existing indices.
- Misbalance Prodeg Index,
- graph,
- fuzzy graph,
- multi-criteria decision-making
Citation: Shama Liaqat, Zeeshan Saleem Mufti, Yilun Shang. Newly defined fuzzy Misbalance Prodeg Index with application in multi-criteria decision-making[J]. AIMS Mathematics, 2024, 9(8): 20193-20220. doi: 10.3934/math.2024984

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Abstract

In crisp graph theory, there are numerous topological indices accessible, including the Misbalance Prodeg Index, which is one of the most well-known degree-based topological indexes. In crisp graphs, both vertices and edges have membership values of $ 1 $ or $ 0 $, whereas in fuzzy graphs, both vertices and edges have different memberships. This is an entire contrast to the crisp graph. In this paper, we introduce the Fuzzy Misbalance Prodeg Index of a fuzzy graph, which is a generalized form of the Misbalance Prodeg Index of a graph. We find bounds of this index and find bounds of certain classes of graphs such as path graph, cycle graph, complete graph, complete bipartite graph, and star graph. We give an algorithm to find the Fuzzy Misbalance Prodeg Index of a graph for the model of multi-criteria decision-making is established. We present applications from daily life in multi-criteria decision-making. We apply our obtained model of the Fuzzy Misbalance Prodeg Index for the multi-criteria decision-making to the choice of the best supplier and we also show the graphical analysis of our index with the other indices that show how our index is better than other existing indices.

References

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