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 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 Vertex Degrees and Isomorphic Properties in Complement of an m-Polar Fuzzy Graph

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Ch. Ramprasad ◽  
P. L. N. Varma ◽  
S. Satyanarayana ◽  
N. Srinivasarao
Keyword(s):  
Graph Theory ◽  
Tensor Product ◽  
Computer Science ◽  
Computational Intelligence ◽  
Cartesian Product ◽  
Combinatorial Problems ◽  
Fuzzy Graph ◽  
Normal Product ◽  
Product Graphs ◽  
Vertex Degrees

Computational intelligence and computer science rely on graph theory to solve combinatorial problems. Normal product and tensor product of an m-polar fuzzy graph have been introduced in this article. Degrees of vertices in various product graphs, like Cartesian product, composition, tensor product, and normal product, have been computed. Complement and μ-complement of an m-polar fuzzy graph are defined and some properties are studied. An application of an m-polar fuzzy graph is also presented in this article.

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 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 Domination of Bipolar Fuzzy Graphs in Various Settings

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Shu Gong ◽  
Gang Hua ◽  
Wei Gao
Keyword(s):  
Dominating Set ◽  
Graph Analysis ◽  
Graph Structure ◽  
Fuzzy Graph ◽  
Dominating Sets ◽  
Critical Position ◽  
Fuzzy Graphs ◽  
Control Set ◽  
Bipolar Fuzzy Sets ◽  
Bipolar Fuzzy Graphs

AbstractBipolar fuzzy sets are used to describe the positive and negative of the uncertainty of objects, and the bipolar fuzzy graphs are used to characterize the structural relationship between uncertain concepts in which the vertices and edges are assigned positive and negative membership function values to feature the opposite uncertainty elevation. The dominating set is the control set of vertices in the graph structure and it occupies a critical position in graph analysis. This paper mainly contributes to extending the concept of domination in the fuzzy graph to the bipolar frameworks and obtaining the related expanded concepts of a variety of bipolar fuzzy graphs. Meanwhile, the approaches to obtain the specific dominating sets are presented. Finally, a numeral example on city data in Yunnan Province is presented to explain the computing of domination in bipolar fuzzy graph in the specific application.

scholarly journals Modeling Imprecise and Bipolar Algebraic and Topological Relations using Morphological Dilations

2021 ◽  
Vol 5 (1) ◽  
pp. 1-20
Author(s):  
Isabelle Bloch
Keyword(s):  
Information Processing ◽  
Fuzzy Sets ◽  
Mathematical Morphology ◽  
Complete Lattice ◽  
Spatial Reasoning ◽  
Topological Relations ◽  
Preference Modeling ◽  
Logical Sense ◽  
Bipolar Fuzzy Sets ◽  
Core Features

Abstract In many domains of information processing, such as knowledge representation, preference modeling, argumentation, multi-criteria decision analysis, spatial reasoning, both vagueness, or imprecision, and bipolarity, encompassing positive and negative parts of information, are core features of the information to be modeled and processed. This led to the development of the concept of bipolar fuzzy sets, and of associated models and tools, such as fusion and aggregation, similarity and distances, mathematical morphology. Here we propose to extend these tools by defining algebraic and topological relations between bipolar fuzzy sets, including intersection, inclusion, adjacency and RCC relations widely used in mereotopology, based on bipolar connectives (in a logical sense) and on mathematical morphology operators. These definitions are shown to have the desired properties and to be consistent with existing definitions on sets and fuzzy sets, while providing an additional bipolar feature. The proposed relations can be used for instance for preference modeling or spatial reasoning. They apply more generally to any type of functions taking values in a poset or a complete lattice, such as L-fuzzy sets.

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
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