A study on irregularity in vague graphs with application in social relations

Considering all physical, biological and social systems, fuzzy graph models serves the elemental processes of all natural and artificial structures. As the indeterminate information is an essential real-life problems, which are mostly uncertain, modelling those problems based on fuzzy graph is highly demanding for an expert. Vague graph can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which fuzzy graphs possibly will not succeed into bringing about satisfactory results. Also, vague graphs are so useful tool to examine many issues such as networking, social systems, geometry, biology, clustering, and traffic plan. Hence, in this paper, we introduce strongly edge irregular vague graphs and strongly edge totally irregular vague graphs. A comparative study between strongly edge irregular vague graphs and strongly edge totally irregular vague graphs is done. Finally, we represent an applicationof irregular vague influence graph to show the importance of irregularity in vague graphs.Publisher's Versio

Interval-valued intuitionistic fuzzy soft graphs with application

The concept of interval-valued intuitionistic fuzzy soft sets and fuzzy graphs structure together constitute a new structure called an interval-valued intuitionistic fuzzy soft graph. The definitions of interval-valued intuitionistic fuzzy soft subgraph and strong interval-valued intuitionistic fuzzy soft graph are introduced with suitable examples. The degree of the good influence of a parameter in a fuzzy network and there is no influence by an interval number in the same system. Similarly, the effectiveness and non-effectiveness of the other fuzzy system on other parameters is measured by the concept of soft graphs in this article. Also, several different types of operations, including Cartesian product, strong product and composition on interval-valued intuitionistic fuzzy soft graphs are presented. Some related properties of these operations are investigated. Finally, we give a real-life application of interval-valued intuitionistic fuzzy soft graphs on social media and find out the most affected person in social media.Publisher's Versio