Most of our conventional tools for formal reasoning, computing, and modeling are precise, deterministic, and crisp. However, many complicated problems in the domains of economics, medicine, engineering, the environment, social science, and other disciplines demand data that is not always precise. We cannot always use traditional approaches because there are so many different types of uncertainty present in these problems. This difficulty could be caused by the parameterization tool’s insufficiency. Soft set theory, which Molodtsov presented in 1999, is a generic mathematical approach for handling uncertain data. Many researchers are currently using soft set theory to solve problems involving decision-making. The concept of soft graphs is used to provide a parameterized point of view for graphs. The topic of graph products has received a lot of interest in graph theory. It is a binary operation on graphs with numerous combinatorial uses. On soft graphs, we can define product operations in a manner similar to how graph products are defined. The co-normal product, the restricted co-normal product, the modular product, and the restricted modular product of soft graphs are all introduced in this study. We prove that these products of soft graphs are again soft graphs and derive methods for computing their vertex count, edge count, and the sum of part degrees.
Soft set is a classification of elements of the universe with respect to some given set of parameters. It is a new approach for modeling vagueness and uncertainty. The concept of soft graph is used to provide a parameterized point of view for graphs. In this paper we introduce the concepts of subdivision graph, power and line graph of a soft graph and investigate some of their properties.
The soft set theory proposed by D. Molodtsov in 1999 is a general mathematical method for dealing with uncertain data. Now many researchers are applying soft set theory in decision making problems. Graph theory is the mathematical study of objects and their pairwise relationships, known as vertices and edges, respectively. The concept of soft graphs is used to provide a parameterized point of view for graphs. Directed graphs can be used to analyze and resolve problems with electrical circuits, project timelines, shortest routes, social links and many other issues. We introduced the notion of the soft directed graph by applying the concepts of soft set in a directed graph. In this paper, we introduce the concept of soft subdigraph and some soft directed graph operations like AND operation, OR operation, soft union, extended union, extended intersection, restricted union and restricted intersection and investigate some of their properties.
Molodtsov proposed soft set theory as a mathematical framework for handling uncertain data. Nowadays, a lot of people employ soft set theory to solve decision making problems. A graph with directed edges is known as a directed graph. Studying and resolving issues with social networks, shortest paths, electrical circuits, etc. using directed graphs is possible. We presented soft directed graphs by extending the notion of soft set to directed graphs. A parameterized perspective for directed graphs is provided by soft directed graphs. In this work, we introduce the rooted product and the restricted rooted product of soft directed graphs and examine some of their properties.
This paper presents an introduction to soft hypergraph operations, namely extended union, extended intersection, restricted union, and restricted intersection, along with the concept of soft semisubhypergraph. We explore various properties of these operations and provide illustrative examples.
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