scholarly journals Fuzzy Graph Structures with Application

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 63 ◽  
Author(s):  
Muzzamal Sitara ◽  
Muhammad Akram ◽  
Muhammad Yousaf Bhatti
Keyword(s):  
General Procedure ◽  
Controversial Issues ◽  
Total Degree ◽  
Graph Structure ◽  
Fuzzy Graph ◽  
Graph Structures ◽  
Degree Of A Vertex

In this article, we introduce the notions of maximal products of fuzzy graph structures, regular fuzzy graph structures, and describe these notions with examples and properties. Further, we present the degree and total degree of a vertex in maximal product of fuzzy graph structures and explain some of their properties. Furthermore, we develop a flowchart to show general procedure of application of fuzzy graph structure, regarding identification of most controversial issues among countries.

scholarly journals Decision-Making Analysis Based on Fuzzy Graph Structures

2020 ◽  
Vol 2020 ◽  
pp. 1-30 ◽  
Author(s):  
Ali N. A. Koam ◽  
Muhammad Akram ◽  
Peide Liu
Keyword(s):  
Decision Making ◽  
General Procedure ◽  
Combinatorial Problems ◽  
Graph Structure ◽  
Fuzzy Graph ◽  
The Road ◽  
Research Article ◽  
Graph Structures ◽  
Fuzzy Graphs ◽  
Degree Of A Vertex

A graph structure is a useful framework to solve the combinatorial problems in various fields of computational intelligence systems and computer science. In this research article, the concept of fuzzy sets is applied to the graph structure to define certain notions of fuzzy graph structures. Fuzzy graph structures can be very useful in the study of various structures, including fuzzy graphs, signed graphs, and the graphs having labeled or colored edges. The notions of the fuzzy graph structure, lexicographic-max product, and degree and total degree of a vertex in the lexicographic-max product are introduced. Further, the proposed concepts are explained through several numerical examples. In particular, applications of the fuzzy graph structures in decision-making process, regarding detection of marine crimes and detection of the road crimes, are presented. Finally, the general procedure of these applications is described by an algorithm.

New concepts of domination in fuzzy graph structures with application

2021 ◽  
pp. 1-13
Author(s):  
A.A. Talebi ◽  
G. Muhiuddin ◽  
S.H. Sadati ◽  
Hossein Rashmanlou
Keyword(s):  
Intelligent Systems ◽  
Dominating Set ◽  
Domination Number ◽  
Graph Structure ◽  
Multiple Relationships ◽  
Fuzzy Graph ◽  
Complex Problems ◽  
Graph Structures ◽  
Fuzzy Graphs ◽  
New Concepts

Fuzzy graphs have a prominent place in the mathematical modelling of the problems due to the simplicity of representing the relationships between topics. Gradually, with the development of science and in encountering with complex problems and the existence of multiple relationships between variables, the need to consider fuzzy graphs with multiple relationships was felt. With the introduction of the graph structures, there was better flexibility than the graph in dealing with problems. By combining a graph structure with a fuzzy graph, a fuzzy graph structure was introduced that increased the decision-making power of complex problems based on uncertainties. The previous definitions restrictions in fuzzy graphs have made us present new definitions in the fuzzy graph structure. The domination of fuzzy graphs has many applications in other sciences including computer science, intelligent systems, psychology, and medical sciences. Hence, in this paper, first we study the dominating set in a fuzzy graph structure from the perspective of the domination number of its fuzzy relationships. Likewise, we determine the domination in terms of neighborhood, degree, and capacity of vertices with some examples. Finally, applications of domination are introduced in fuzzy graph structure.

scholarly journals Certain Concepts inm-Polar Fuzzy Graph Structures

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Akram ◽  
Noura Alshehri ◽  
Rabia Akmal
Keyword(s):  
Fuzzy Sets ◽  
Graph Structure ◽  
Fuzzy Graph ◽  
Cut Vertex ◽  
Graph Structures

We apply the concept ofm-polar fuzzy sets to graph structures. We introduce certain concepts inm-polar fuzzy graph structures, including strongm-polar fuzzy graph structure,m-polar fuzzyDi-cycle,m-polar fuzzyDi-tree,m-polar fuzzyDi-cut vertex, andm-polar fuzzyDi-bridge, and we illustrate these concepts by several examples. We present the notions ofϕ-complement of anm-polar fuzzy graph structure and self-complementary, strong self-complementary, totally strong self-complementarym-polar fuzzy graph structures, and we investigate some of their properties.

scholarly journals Product Operations on q-Rung Orthopair Fuzzy Graphs

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 588 ◽  
Author(s):  
Songyi Yin ◽  
Hongxu Li ◽  
Yang Yang
Keyword(s):  
Direct Product ◽  
Cartesian Product ◽  
Total Degree ◽  
Fuzzy Graph ◽  
Lexicographic Product ◽  
Intuitionistic Fuzzy ◽  
Strong Product ◽  
Fuzzy Graphs ◽  
Degree Of A Vertex

The q-rung orthopair fuzzy graph is an extension of intuitionistic fuzzy graph and Pythagorean fuzzy graph. In this paper, the degree and total degree of a vertex in q-rung orthopair fuzzy graphs are firstly defined. Then, some product operations on q-rung orthopair fuzzy graphs, including direct product, Cartesian product, semi-strong product, strong product, and lexicographic product, are defined. Furthermore, some theorems about the degree and total degree under these product operations are put forward and elaborated with several examples. In particular, these theorems improve the similar results in single-valued neutrosophic graphs and Pythagorean fuzzy graphs.

scholarly journals Application of Bipolar Fuzzy Sets in Graph Structures

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Muhammad Akram ◽  
Rabia Akmal
Keyword(s):  
Computer Science ◽  
Fuzzy Sets ◽  
Computational Intelligence ◽  
Combinatorial Problems ◽  
Graph Structure ◽  
Fuzzy Graph ◽  
Cut Vertex ◽  
Graph Structures ◽  
Bipolar Fuzzy Sets

A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we apply the concept of bipolar fuzzy sets to graph structures. We introduce certain notions, including bipolar fuzzy graph structure (BFGS), strong bipolar fuzzy graph structure, bipolar fuzzyNi-cycle, bipolar fuzzyNi-tree, bipolar fuzzyNi-cut vertex, and bipolar fuzzyNi-bridge, and illustrate these notions by several examples. We studyϕ-complement, self-complement, strong self-complement, and totally strong self-complement in bipolar fuzzy graph structures, and we investigate some of their interesting properties.

scholarly journals Complement of max product of intuitionistic fuzzy graphs

2021 ◽  
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Hamming Distance ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Degree Of A Vertex ◽  
Intuitionistic Fuzzy Graphs

AbstractIn this paper, the complement of max product of two intuitionistic fuzzy graphs is defined. The degree of a vertex in the complement of max product of intuitionistic fuzzy graph is studied. Some results on complement of max product of two regular intuitionistic fuzzy graphs are stated and proved. Finally, we provide an application of intuitionistic fuzzy graphs in school determination using normalized Hamming distance.

A Scheme for Numerical Representation of Graph Structures in Engineering Design

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
David F. Wyatt ◽  
David C. Wynn ◽  
P. John Clarkson
Keyword(s):  
Engineering Design ◽  
Design Problem ◽  
Structure Design ◽  
Numerical Representation ◽  
Graph Structure ◽  
Numerical Techniques ◽  
Mathematical Properties ◽  
Conversion Algorithm ◽  
Graph Structures ◽  
Improve Access

Graph structures are fundamental in many aspects of design. This paper discusses a way to improve access to design spaces of graph structures, by converting graph structures into numerical values and vice versa. Mathematical properties of such conversions are described, and those that are desirable are identified. A candidate conversion algorithm, Indexed Stacked Blocks, is proposed. Its use and benefits are illustrated through an example graph-structure design problem. The example demonstrates that such conversions allow design spaces of graph structures to be visualized, sampled, and evaluated. In principle, they also allow other powerful numerical techniques to be applied to the design of graph-structure-based systems.

scholarly journals Fuzzy Graph Structures: A Generalised Approach

2011 ◽  
Vol 6 (3) ◽  
pp. 363-370
Author(s):  
Dinesh T. ◽  
Ramakrishnan T.V.
Keyword(s):  
Fuzzy Graph ◽  
Graph Structures

Certain Types of Fuzzy Soft Graphs

2018 ◽  
Vol 14 (02) ◽  
pp. 145-156 ◽  
Author(s):  
Anas Al-Masarwah ◽  
Majdoleen Abu Qamar
Keyword(s):  
Total Degree ◽  
Degree Of A Vertex

In this paper, we introduce the concepts of uniform vertex fuzzy soft graphs, uniform edge fuzzy soft graphs, degree of a vertex, total degree of a vertex and complement fuzzy soft graphs with some examples. Also, we study regular and totally regular fuzzy soft graphs, and the conditions under which the complement of regular fuzzy soft graph becomes regular as well as totally regular are discussed. Also, we obtain some results related to regular, totally regular and complete fuzzy soft graphs.

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