• Annals of Fuzzy Mathematics and Informatics
• /
• v.16 no.3
• /
• pp.363-371
• /
• 2018

The main objective of this paper is to connect fuzzy theory, graph theory and fuzzy graph theory with algebraic structure. We introduce the notion of fuzzy graph of semigroup, the notion of fuzzy ideal graph of semigroup as a generalization of fuzzy ideal of semigroup, intuitionistic fuzzy ideal of semigroup, fuzzy graph and graph, the notion of isomorphism of fuzzy graphs of semigroups and regular fuzzy graph of semigroup and we study some of their properties.

• Journal of applied mathematics & informatics
• /
• v.41 no.5
• /
• pp.1145-1153
• /
• 2023

The notion of maximal product of two fuzzy graphs was introduced by Radha and Arumugam in 2015 and the notion of balanced fuzzy graph was introduced by Al-Hawary in 2011. In this paper, we give a modification of the maximal product definition, which we call maximal strong product. We also introduce the relatively new notion of maximal-balanced fuzzy graphs. We give necessary and sufficient conditions for the maximal strong product of two balanced (resp., maximal-balanced) fuzzy graphs to be balanced (resp., maximal-balanced) and we prove that these two independent notions are preserved under isomorphism.

• Korean Journal of Mathematics
• /
• v.31 no.4
• /
• pp.485-494
• /
• 2023

The degree of hesitancy of a vertex in a hesitancy fuzzy graph depends on the degree of membership and non-membership of the vertex. We define a new class of hesitancy fuzzy graph, the intuitionistic hesitancy fuzzy graph in which the degree of hesitancy of a vertex is independent of the degree of its membership and non-membership. We introduce the idea of β-product of a pair of hesitancy fuzzy graphs and intuitionistic hesitancy fuzzy graphs and prove certain results based on this product.

• Journal of applied mathematics & informatics
• /
• v.42 no.1
• /
• pp.123-137
• /
• 2024

In this paper, Power fuzzy graphs is newly introduced by allotting fuzzy values on power graphs in such a way that the newly added edges, has the edge membership values between a closed interval which depends on vertex membership values and the length of the added edges. Power fuzzy subgraphs and total power fuzzy graphs are newly defined with properties and some special cases. It is observed that every power fuzzy graph is a fuzzy graph but the converse need not be true. Edges that are incident to vertices with the least vertex membership values are retained in the least power fuzzy subgraph. Further, the application of these concepts in real life time has been presented and discussed using power fuzzy graph model.

• Journal of applied mathematics & informatics
• /
• v.34 no.1_2
• /
• pp.49-60
• /
• 2016

In this paper, two different approaches to chromatic number of a bipolar fuzzy graph are introduced. The first approach is based on the α-cuts of a bipolar fuzzy graph and the second approach is based on the definition of Eslahchi and Onagh for chromatic number of a fuzzy graph. Finally, the bipolar fuzzy vertex chromatic number and the edge chromatic number of a complete bipolar fuzzy graph, characterized.

• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.1043-1052
• /
• 2022

Our goal in this paper is to propose the advancement proposed by Alsina, Klement and other researchers in the area of fuzzy logic applied to the area of fuzzy graph theory. We introduce the notion of complete Hamacher fuzzy graphs and the notion of balanced Hamacher fuzzy graphs and discuss their properties. Moreover, several operations on these fuzzy graphs are explored via the complete notion.

• Journal of applied mathematics & informatics
• /
• v.35 no.1_2
• /
• pp.95-111
• /
• 2017

Recently, interval-valued fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they allowed the degree of membership of a vertex to an edge to be represented by interval values in [0.1] rather than the crisp values between 0 and 1. In this paper, we introduce the concepts of regular and totally regular interval-valued fuzzy graphs and discusses some properties of the ${\mu}$-complement of interval-valued fuzzy graph. Self ${\mu}$-complementary interval-valued fuzzy graphs and self-weak ${\mu}$-complementary interval-valued fuzzy graphs are defined and a necessary condition for an interval valued fuzzy graph to be self ${\mu}$-complementary is discussed. We define busy vertices and free vertices in interval valued fuzzy graph and study their image under an isomorphism.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.2 no.2
• /
• pp.153-158
• /
• 2002

In this paper we introduce the concept of a fuzzy almost c-continuity and investigate some of its properties.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2002.05a
• /
• pp.285-288
• /
• 2002

In this paper, we introduce the concept of a fuzzy almost c-continuity and investigate some of its properties.

• Journal of applied mathematics & informatics
• /
• v.34 no.3_4
• /
• pp.179-192
• /
• 2016

In this paper, we introduce product interval-valued fuzzy graphs and prove several results which are analogous to interval-valued fuzzy graphs. We conclude by giving properties for a product interval-valued fuzzy graph.