Interval-valued intuitionistic fuzzy soft graph

One of the theories designed to deal with uncertainty is the soft set theory. These collections were used due to a lack of membership functions in the fields of decision-making, systems analysis, classification, data mining, medical diagnosis, etc. Fuzzy graphs based on soft sets were developed alongside fuzzy graphs. Studying these graphs, examining the properties and operators on it, give special flexibility in dealing with indeterminate problems. In particular, most of the issues around us are mixed and operations are conveniently used in many combinatorial applications. Therefore, the study of operations have a significant effect on solving problems based on decisionmaking, medical, etc. In this paper, we introduce the notion of interval-valued intuitionistic fuzzy soft graphs, by combine concepts of interval-valued intuitionistic fuzzy graphs and fuzzy soft graphs. We also present several different types of operations including cartesian product, strong product and composition on interval-valued intuitionistic fuzzy soft graphs and investigate some properties of them.Publisher's Versio

Generarlized Operations on Fuzzy Graphs

To discuss the Cartesian Product Composition, union and join on Interval-valued fuzzy graphs.  We also introduce the notion of Interval-valued fuzzy complete graphs.  Some properties of self complementary graph. Key Words : Interval-valued fuzzy graph self complementary Interval valued fuzzy complete graph

On some operations and density of m-polar fuzzy graphs

AbstractThe theoretical concepts of graphs are highly utilized by computer science applications, social sciences, and medical sciences, especially in computer science for applications such as data mining, image segmentation, clustering, image capturing, and networking. Fuzzy graphs, bipolar fuzzy graphs and the recently developed m-polar fuzzy graphs are growing research topics because they are generalizations of graphs (crisp). In this paper, three new operations, i.e., direct product, semi-strong product and strong product, are defined on m-polar fuzzy graphs. It is proved that any of the products of m-polar fuzzy graphs are again an m-polar fuzzy graph. Sufficient conditions are established for each to be strong, and it is proved that the strong product of two complete m-polar fuzzy graphs is complete. If any of the products of two m-polar fuzzy graphs G1 and G2 are strong, then at least G1 or G2 must be strong. Moreover, the density of an m-polar fuzzy graph is defined, the notion of balanced m-polar fuzzy graph is studied, and necessary and sufficient conditions for the preceding products of two m-polar fuzzy balanced graphs to be balanced are established. Finally, the concept of product m-polar fuzzy graph is introduced, and it is shown that every product m-polar fuzzy graph is an m-polar fuzzy graph. Some operations, like union, direct product, and ring sum are defined to construct new product m-polar fuzzy graphs

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

On bipolar complex intuitionistic fuzzy graphs

In the present article, we devised the novel approach on the bipolar complex intuitionistic fuzzy set, bipolar complex intuitionistic fuzzy graphs and operations namely composition, cartesian product, join and union of the bipolar complex intuitionistic fuzzy graphs are elucidated with certain examples. Finally, the notions of isomorphisms and complement of bipolar complex intuitionistic fuzzy graphs are established and reviewed many of its characteristics.Publisher's Versio

Some Operations on Complex Fuzzy Graphs

In this paper we discussed about some types of complex fuzzygraphs which is the extension of fuzzy graph. As the membershipvalue of elements of fuzzy graph is in between 0 and 1. In complexfuzzy graph it will be extended to unit circle of complex plane. Someoperations such as union, intersection, composition, cartesian productof two complex fuzzy graphs are introduced. Some basic theoremswith respect to the above mentioned operations are proved with examples

Derivable Single Valued Neutrosophic Graphs Based on KM-Fuzzy Metric

In this paper we consider the concept of KM-fuzzy metric spaces and we introduce a novel concept of KM-single valued neutrosophic metric graphs based on KM-fuzzy metric spaces. Then we investigate the finite KM-fuzzy metric spaces with respect to KM-fuzzy metrics and we construct the KMfuzzy metric spaces on any given non-empty sets. We try to extend the concept of KM-fuzzy metric spaces to a larger class of KM-fuzzy metric spaces such as union and product of KM-fuzzy metric spaces and in this regard we investigate the class of products of KM-single valued neutrosophic metric graphs. In the final, we define some operations such as tensor product, Cartesian product, semi-strong product, strong product, union, semi-ring sum, suspension, and complement of KM-single valued neutrosophic metric graphs