scholarly journals Connectivity Indices of Intuitionistic Fuzzy Graphs and Their Applications in Internet Routing and Transport Network Flow

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Tulat Naeem ◽  
Abdu Gumaei ◽  
Muhammad Kamran Jamil ◽  
Ahmed Alsanad ◽  
Kifayat Ullah
Keyword(s):  
Network Flow ◽  
Real Life ◽  
Vital Role ◽  
Transport Network ◽  
Internet Routing ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Connectivity Indices ◽  
Intuitionistic Fuzzy Graphs

Connectivity index CI has a vital role in real-world problems especially in Internet routing and transport network flow. Intuitionistic fuzzy graphs IFGs allow to describe two aspects of information using membership and nonmembership degrees under uncertainties. Keeping in view the importance of CI s in real life problems and comprehension of IFGs , we aim to develop some CI s in the environment of IFGs . We introduce two types of CI s , namely, CI and average CI , in the frame of IFGs . In spite of that, certain kinds of nodes called IF connectivity enhancing node IFCEN , IF connectivity reducing node IFCRN , and IF neutral node are introduced for IFGs . We have introduced strongest strong cycles, θ -evaluation of vertices, cycle connectivity, and CI of strong cycle. Applications of the CI s in two different types of networks are done, Internet routing and transport network flow, followed by examples to show the applicability of the proposed work.

scholarly journals Graphical Analysis of Covering and Paired Domination in the Environment of Neutrosophic Information

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Sami Ullah Khan ◽  
Abdul Nasir ◽  
Naeem Jan ◽  
Zhen-Hua Ma
Keyword(s):  
Graph Theory ◽  
Optimization Problems ◽  
Domination Number ◽  
Real Life ◽  
Graphical Analysis ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Neutrosophic Graph ◽  
Paired Domination ◽  
Intuitionistic Fuzzy Graphs

Neutrosophic graph (NG) is a powerful tool in graph theory, which is capable of modeling many real-life problems with uncertainty due to unclear, varying, and indeterminate information. Meanwhile, the fuzzy graphs (FGs) and intuitionistic fuzzy graphs (IFGs) may not handle these problems as efficiently as NGs. It is difficult to model uncertainty due to imprecise information and vagueness in real-world scenarios. Many real-life optimization problems are modeled and solved using the well-known fuzzy graph theory. The concepts of covering, matching, and paired domination play a major role in theoretical and applied neutrosophic environments of graph theory. Henceforth, the current study covers this void by introducing the notions of covering, matching, and paired domination in single-valued neutrosophic graph (SVNG) using the strong edges. Also, many attention-grabbing properties of these concepts are studied. Moreover, the strong covering number, strong matching number, and the strong paired domination number of complete SVNG, complete single-valued neutrosophic cycle (SVNC), and complete bipartite SVNG are worked out along with their fascinating properties.

scholarly journals New Concepts of Picture Fuzzy Graphs with Application

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 470 ◽  
Author(s):  
Cen Zuo ◽  
Anita Pal ◽  
Arindam Dey
Keyword(s):  
Fuzzy Set ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Strong Product ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Picture Fuzzy Set

The picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, in which a intuitionistic fuzzy set may fail to reveal satisfactory results. Picture fuzzy set is an extension of the classical fuzzy set and intuitionistic fuzzy set. It can work very efficiently in uncertain scenarios which involve more answers to these type: yes, no, abstain and refusal. In this paper, we introduce the idea of the picture fuzzy graph based on the picture fuzzy relation. Some types of picture fuzzy graph such as a regular picture fuzzy graph, strong picture fuzzy graph, complete picture fuzzy graph, and complement picture fuzzy graph are introduced and some properties are also described. The idea of an isomorphic picture fuzzy graph is also introduced in this paper. We also define six operations such as Cartesian product, composition, join, direct product, lexicographic and strong product on picture fuzzy graph. Finally, we describe the utility of the picture fuzzy graph and its application in a social network.

scholarly journals On Certain Products of Complex Intuitionistic Fuzzy Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Abida Anwar ◽  
Faryal Chaudhry
Keyword(s):  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Specific Information ◽  
Intuitionistic Fuzzy ◽  
Modular Product ◽  
Fuzzy Graphs ◽  
Degree Of A Vertex ◽  
Wide Range ◽  
Complex Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Graphs

A complex intuitionistic fuzzy set (CIFS) can be used to model problems that have both intuitionistic uncertainty and periodicity. A diagram composed of nodes connected by lines and labeled with specific information may be used to depict a wide range of real-life and physical events. Complex intuitionistic fuzzy graphs (CIFGs) are a broader type of diagram that may be used to manipulate data. In this paper, we define the key operations direct, semistrong, strong, and modular products for complex intuitionistic fuzzy graphs and look at some interesting findings. Further, the strong complex intuitionistic fuzzy graph is defined, and several significant findings are developed. Furthermore, we study the behavior of the degree of a vertex in the modular product of two complex intuitionistic fuzzy graphs.

scholarly journals ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1456
Author(s):  
Stefka Fidanova ◽  
Krassimir Todorov Atanassov
Keyword(s):  
Decision Making ◽  
Knapsack Problem ◽  
Propositional Logic ◽  
Optimization Problems ◽  
Real Life ◽  
Combinatorial Optimization Problems ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Multiple Constraint

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the nature, when they look for a food. One of the algorithm parameters is called pheromone, and it is updated every iteration according quality of the achieved solutions. The intuitionistic fuzzy (propositional) logic was introduced as an extension of Zadeh’s fuzzy logic. In it, each proposition is estimated by two values: degree of validity and degree of non-validity. In this paper, we propose two variants of intuitionistic fuzzy pheromone updating. We apply our ideas on Multiple-Constraint Knapsack Problem (MKP) and compare achieved results with traditional ACO.

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.

scholarly journals An Intuitionistic Fuzzy Graph’s Signless Laplacian Energy

2018 ◽  
Vol 7 (4.10) ◽  
pp. 892
Author(s):  
Obbu Ramesh ◽  
S. Sharief Basha
Keyword(s):  
Adjacency Matrix ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Laplacian Energy ◽  
Signless Laplacian ◽  
Intuitionistic Fuzzy Graphs

We are extending concept into the Intuitionistic fuzzy graph’ Signless Laplacian energy  instead of the Signless Laplacian energy of fuzzy graph. Now we demarcated an Intuitionistic fuzzy graph’s Signless adjacency matrix and also  an Intuitionistic fuzzy graph’s Signless Laplacian energy. Here we find the Signless Laplacian energy ‘s Intuitionistic fuzzy graphs above and below   boundaries of   an with suitable examples.   

scholarly journals Perfectly Regular and Perfectly Edge-Regular Intuitionistic Fuzzy Graphs

2019 ◽  
Vol 9 (1) ◽  
pp. 6348-6352
Keyword(s):  
Spectral Properties ◽  
Constant Function ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Intuitionistic Fuzzy Graphs

A Perfectly regular intuitionistic fuzzy graph is an intuitionistic fuzzy graph that is both regular and totally regular. In this paper we introduce and classify these types of intuitionistic fuzzy graphs and study several of their properties, including how two classes of intuitionistic fuzzy graphs structurally relate to one another and several of their spectral properties such as isospectral intuitionistic fuzzy graphs and when the energy of intuitionistic fuzzy graph is proportional to the energy of their underlying crisp graphs. These properties are studied in particular due to having at least one constant function and .

scholarly journals Specific Types of Pythagorean Fuzzy Graphs and Application to Decision-Making

2018 ◽  
Vol 23 (3) ◽  
pp. 42 ◽  
Author(s):  
Muhammad Akram ◽  
Amna Habib ◽  
Farwa Ilyas ◽  
Jawaria Dar
Keyword(s):  
Decision Making ◽  
Research Study ◽  
Symmetric Difference ◽  
Intuitionistic Fuzzy ◽  
Research Article ◽  
Fuzzy Graphs ◽  
Intuitionistic Fuzzy Graphs

The purpose of this research study is to present some new operations, including rejection, symmetric difference, residue product, and maximal product of Pythagorean fuzzy graphs (PFGs), and to explore some of their properties. This research article introduces certain notions, including intuitionistic fuzzy graphs of 3-type (IFGs3T), intuitionistic fuzzy graphs of 4-type (IFGs4T), and intuitionistic fuzzy graphs of n-type (IFGsnT), and proves that every IFG(n−1)T is an IFGnT (for n ≥ 2). Moreover, this study discusses the application of Pythagorean fuzzy graphs in decision making.

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