• East Asian mathematical journal
• /
• v.23 no.1
• /
• pp.1-8
• /
• 2007

In this paper, we introduce the concept of strong and weak domination in fuzzy graphs, and provide some examples to explain various notions introduced. Also some properties discussed.

• Communications of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.803-819
• /
• 2024

In our study, the integration of fuzzy graphs into classical graph theory gives rise to a novel concept known as "Fuzzy Super Subdivision." Let SS_f (G) be the fuzzy super subdivision graphs, by substituting a complete bipartite graph k_(2,m) (m = 1, 2, . . .) for each edge of a fuzzy graph. The attributes and properties of this newly proposed concept are briefly outlined, in addition to illustrative examples. Furthermore, significant findings are discussed on connectivity, size, degree and order of fuzzy super subdivision structures. To illustrate the practical implications of our approach, we present an application focused on analyzing the growth of infections in blood or urine samples using the Fuzzy Super Subdivision model.

• 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.

• Journal of applied mathematics & informatics
• /
• v.42 no.4
• /
• pp.739-748
• /
• 2024

The intention of this paper is to acquaint domination, total domination on bipolar intuitionistic fuzzy graphs. Subsequently for bipolar intuitionistic fuzzy graphs the domination number and the total domination number are defined. Consequently we proved necessary and sufficient condition for a d-set to be minimal d-set, bounds for domination number and equality conditions for domination number and order.

• Journal of applied mathematics & informatics
• /
• v.33 no.5_6
• /
• pp.545-557
• /
• 2015

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G₁ and G₂ using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.

• Annals of Fuzzy Mathematics and Informatics
• /
• v.16 no.3
• /
• pp.301-316
• /
• 2018

In this paper, the concept of connected geodesic number, $gn_c(G)$, of a fuzzy graph G is introduced and its limiting bounds are identified. It is proved that all extreme nodes of G and all cut-nodes of the underlying crisp graph $G^*$ belong to every connected geodesic cover of G. The connected geodesic number of complete fuzzy graphs, fuzzy cycles, fuzzy trees and of complete bipartite fuzzy graphs are obtained. It is proved that for any pair k, n of integers with $3{\leq}k{\leq}n$, there exists a connected fuzzy graph G : (V, ${\sigma}$, ${\mu}$) on n nodes such that $gn_c(G)=k$. Also, for any positive integers $2{\leq}a<b{\leq}c$, it is proved that there exists a connected fuzzy graph G : (V, ${\sigma}$, ${\mu}$) such that the geodesic number gn(G) = a and the connected geodesic number $gn_c(G)=b$.

• Communications of the Korean Mathematical Society
• /
• v.18 no.2
• /
• pp.325-340
• /
• 2003

We introduce a fuzzy g-closure operator induced by a fuzzy topological space in view of the definition of Sostak [13]. We show that it is a fuzzy closure operator. Furthermore, it induces a fuzzy topology which is finer than a given fuzzy topology. We investigate some properties of fuzzy g-closure operators.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1993.06a
• /
• pp.1402-1405
• /
• 1993

In this paper, a fault evaluation method is proposed, which is to determine whether analog electronic circuits are faulty or not. In our method, evaluation characteristics of an expert test engineer are defined by means of directed graphs. By performing a multi-stage fuzzy inference based on the graphs, novice test engineers can derive a fault evaluation result satisfied by the expert. The effectiveness of our method is checked by some experiments for an amplifier circuit.

• Journal of applied mathematics & informatics
• /
• v.42 no.2
• /
• pp.283-290
• /
• 2024

In this article, a new operation on product fuzzy graphs (PFGs) is provide; namely β-product. We give sufficient conditions for the β-product of two PFGs to be strong and we prove if the β-product of two PFGs is complete, then one of them is strong. We also study the unbiased notion of the class of PFGs and necessary and sufficient conditions for the β-product to be unbiased are given.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.12 no.6
• /
• pp.565-570
• /
• 2002

We introduce the concepts of fuzzy H-continuity and fuzzy strongly closed graph, respectively and investigate some of their properties.