• Journal of applied mathematics & informatics
• /
• v.32 no.5_6
• /
• pp.827-842
• /
• 2014

In this paper, we introduce the notion of Cayley intuitionistic fuzzy graphs and investigate some of their properties. We present some interesting properties of intuitionistic fuzzy graphs in terms of algebraic structures. We discuss connectedness in Cayley intuitionistic fuzzy graphs. We also describe different types of ${\alpha}$-connectedness in Cayley intuitionistic fuzzy graphs.

• 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.

• 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.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.

• 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.

• 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.

• Communications of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.1077-1097
• /
• 2017

In this research article, we introduce certain concepts, including domination, total domination, strong domination, weak domination, edge domination and total edge domination in m-polar fuzzy graphs. We describe these concepts by several examples. We investigate some related properties of certain dominations in m-polar fuzzy graphs. We also present a decision making method based on domination in m-polar fuzzy graphs.

• Communications of the Korean Mathematical Society
• /
• v.21 no.3
• /
• pp.587-593
• /
• 2006

The notion of intuitionistic fuzzy graphs is introduced. We show how to associate an intuitionistic fuzzy sub(semi)group with an intuitionistic fuzzy graph in a natural way.

• Journal of Digital Convergence
• /
• v.11 no.11
• /
• pp.409-414
• /
• 2013

Naive Bayesian classifiers are a powerful and well-known type of classifiers that can be easily induced from a dataset of sample cases. However, the strong conditional independence assumptions can sometimes lead to weak classification performance. Normally, naive Bayesian classifiers use Gaussian distributions to handle continuous attributes and to represent the likelihood of the features conditioned on the classes. The probability density of attributes, however, is not always well fitted by a Gaussian distribution. Another eminent type of classifier is the neuro-fuzzy classifier, which can learn fuzzy rules and fuzzy sets using supervised learning. Since there are specific structural similarities between a neuro-fuzzy classifier and a naive Bayesian classifier, the purpose of this study is to apply learning distribution graphs constructed by a neuro-fuzzy network to naive Bayesian classifiers. We compare the Gaussian distribution graphs with the fuzzy distribution graphs for the naive Bayesian classifier. We applied these two types of distribution graphs to classify leukemia and colon DNA microarray data sets. The results demonstrate that a naive Bayesian classifier with fuzzy distribution graphs is more reliable than that with Gaussian distribution graphs.