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Fuzzy Information and Engineering 2023, 15(3): 248-273 https://doi.org/10.26599/FIE.2023.9270019
Article | Open Access | Issue | Published: 01 September 2023

Certain Concepts in Directed Rough Fuzzy Graphs and Application to Mergers of Companies

Show Author's Information Iqra Nawaz1 ,  Uzma Ahmad1( )
Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
Keywords:
composition, directed rough fuzzy graph, indegree of vertex, outdegree of vertex, union
Cite this article:
Nawaz I, Ahmad U. Certain Concepts in Directed Rough Fuzzy Graphs and Application to Mergers of Companies. Fuzzy Information and Engineering, 2023, 15(3): 248-273. https://doi.org/10.26599/FIE.2023.9270019
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Abstract Full text About this article

A directed rough fuzzy graph (DRFG) is a unique and innovative hybrid model because it deals with more complex problems of uncertainty in the presence of incomplete data information or rough universe. A DRFG can be obtained from two given DRFGs by union, Cartesian product and composition. When we study operations for DRFGs with a large number of vertices, the degree of vertices in a DRFG presents a confusing picture. Therefore, a mechanism for determining the degree of vertices for DRFG operations is needed. The main objective of this study is to analyze and investigate the degree of vertices in DRFGs formed by certain operations, which will provide clear explanations of operations on DRFGs and their effects on vertex degrees with examples. In this paper, we find the degree of a vertex in DRFGs formed by these operations in terms of the degree of vertices in the given DRFGs in some special cases. We explain these operations with some examples. In addition, we provide an application to the corporate merger problem to test our approach and obtain an optimal result. We have developed two algorithms to elaborate the procedure for our application. Finally, we created a comparison table comparing our results for Algorithms 1 and 2 for the same enterprise merger network.


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About this article

Certain Concepts in Directed Rough Fuzzy Graphs and Application to Mergers of Companies

Show Author's information Iqra Nawaz1 , Uzma Ahmad1( )
Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan

Abstract

A directed rough fuzzy graph (DRFG) is a unique and innovative hybrid model because it deals with more complex problems of uncertainty in the presence of incomplete data information or rough universe. A DRFG can be obtained from two given DRFGs by union, Cartesian product and composition. When we study operations for DRFGs with a large number of vertices, the degree of vertices in a DRFG presents a confusing picture. Therefore, a mechanism for determining the degree of vertices for DRFG operations is needed. The main objective of this study is to analyze and investigate the degree of vertices in DRFGs formed by certain operations, which will provide clear explanations of operations on DRFGs and their effects on vertex degrees with examples. In this paper, we find the degree of a vertex in DRFGs formed by these operations in terms of the degree of vertices in the given DRFGs in some special cases. We explain these operations with some examples. In addition, we provide an application to the corporate merger problem to test our approach and obtain an optimal result. We have developed two algorithms to elaborate the procedure for our application. Finally, we created a comparison table comparing our results for Algorithms 1 and 2 for the same enterprise merger network.

Keywords: composition, directed rough fuzzy graph, indegree of vertex, outdegree of vertex, union

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Received: 16 February 2023
Revised: 29 May 2023
Accepted: 18 June 2023
Published: 01 September 2023
Issue date: September 2023

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© The Author(s) 2023. Published by Tsinghua University Press.

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This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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