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.
Highlights
For solving many problems involving uncertainty and vagueness in engineering, social sciences, economics, computers sciences and in several other areas, our traditional classical methods are not always absolutely effective
It is shown that the MSR-graphs are more precise and finer than soft rough graphs
A graph G ∗ is a triple consisting of a vertex set V ( G ∗ ), an edge set E ( G ∗ ), and a relation that associates with each edge two vertices called its endpoints
Summary
For solving many problems involving uncertainty and vagueness in engineering, social sciences, economics, computers sciences and in several other areas, our traditional classical methods are not always absolutely effective. An effort is made by [49] to establish some kind of linkage and to discuss the uncertainty in soft graphs He introduced the concept of soft rough graphs, where instead of equivalence classes, parameterized subsets of vertices and edges serve the aim of finding the lower and upper approximations. In such process, some unusual situations may occur like the upper approximation of a non-empty vertex/edge set may be empty.
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