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Symmetry 2018, 10(5), 145; https://doi.org/10.3390/sym10050145

Another Approach to Roughness of Soft Graphs with Applications in Decision Making

1,†,* , 1,†
,
2,†
and
3,†
1
Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad 44000, Pakistan
2
Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
3
Department of Mathematics, Islamabad Model College for Girls, F-6/2, Islamabad 44000, Pakistan
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 23 March 2018 / Revised: 17 April 2018 / Accepted: 28 April 2018 / Published: 7 May 2018
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Abstract

Fuzzy sets, rough sets and soft sets are different tools for modeling problems involving uncertainty. Graph theory is another powerful tool for representing the information by means of diagrams, matrices or relations. A possible amalgamation of three different concepts rough sets, soft sets and graphs, known as soft rough graphs, is proposed by Noor et al. They introduced the notion of vertex, edge induced soft rough graphs and soft rough trees depending upon the parameterized subsets of vertex set and edge set. In this article, a new framework for studying the roughness of soft graphs in more general way is introduced. This new model is known as the modified soft rough graphs or MSR -graphs. The concept of the roughness membership function of vertex sets, edge sets and of a graph is also introduced. Further, it has been shown that MSR -graphs are more robust than soft rough graphs. Some results, which are not handled by soft rough graphs, can be handled by modified soft rough graphs. The notion of uncertainty measurement associated with MSR -graphs is introduced. All applications related to decision makings are only restricted to the information of individuals only, not their interactions, using this technique we are able to involve the interactions (edges) of individuals with each other that enhanced the accuracy in decisions. View Full-Text
Keywords: soft rough graphs; modified soft rough graphs; graph approximation space; uncertainty; decision making soft rough graphs; modified soft rough graphs; graph approximation space; uncertainty; decision making
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Shah, N.; Rehman, N.; Shabir, M.; Irfan Ali, M. Another Approach to Roughness of Soft Graphs with Applications in Decision Making. Symmetry 2018, 10, 145.

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