On Laplacian energy of picture fuzzy graphs in site selection problem

2021 ◽  
pp. 1-18
Author(s):  
Mahima Poonia ◽  
Rakesh Kumar Bajaj
Keyword(s):  
Decision Making ◽  
Site Selection ◽  
Upper Bounds ◽  
Selection Problem ◽  
Hydropower Plant ◽  
Fuzzy Graph ◽  
Fuzzy Information ◽  
Fuzzy Graphs ◽  
Laplacian Energy ◽  
Selection For

In the present work, the adjacency matrix, the energy and the Laplacian energy for a picture fuzzy graph/directed graph have been introduced along with their lower and the upper bounds. Further, in the selection problem of decision making, a methodology for the ranking of the available alternatives has been presented by utilizing the picture fuzzy graph and its energy/Laplacian energy. For the shake of demonstrating the implementation of the introduced methodology, the task of site selection for the hydropower plant has been carried out as an application. The originality of the introduced approach, comparative remarks, advantageous features and limitations have also been studied in contrast with intuitionistic fuzzy and Pythagorean fuzzy information.

scholarly journals Applications of graph’s complete degree with bipolar fuzzy information

2021 ◽  
Author(s):  
Soumitra Poulik ◽  
Ganesh Ghorai
Keyword(s):  
Decision Making ◽  
Cold War ◽  
Communication System ◽  
Communication Systems ◽  
Open Neighborhood ◽  
Fuzzy Graph ◽  
Fuzzy Information ◽  
Fuzzy Graphs ◽  
Bipolar Fuzzy Graphs ◽  
The Relationship

AbstractDue to the presence of two opposite directional thinking in relationships between countries and communication systems, the systems may not always be balanced. Therefore, the perfectness between countries relations are highly important. It comes from how much they were connected to each other for communication. In this study, first perfectly regular bipolar fuzzy graph is introduced and examined the regularity of nodes. Then, the relationship between the adjacent nodes and their regularity are visualized as a perfectly edge-regular bipolar fuzzy graphs. The totally accurate communication between all connected nodes is explained by introducing completely open neighborhood degree and completely closed neighborhood degree of nodes and edges in a bipolar fuzzy graph. Some algorithms and flowcharts of the proposed methods are given. Finally, two applications of these cogitation are exhibited in two bipolar fuzzy fields. The first one is in international relationships between some countries during cold-war era and the second one is in decision-making between teachers–students communication system for the improvement of teaching.

scholarly journals Energy of Pythagorean Fuzzy Graphs with Applications

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 136 ◽  
Author(s):  
Muhammad Akram ◽  
Sumera Naz
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Satellite Communication ◽  
Research Study ◽  
Upper Bounds ◽  
Intuitionistic Fuzzy Sets ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs ◽  
Laplacian Energy ◽  
Duality Property

Pythagorean fuzzy sets (PFSs), an extension of intuitionistic fuzzy sets (IFSs), inherit the duality property of IFSs and have a more powerful ability than IFSs to model the obscurity in practical decision-making problems. In this research study, we compute the energy and Laplacian energy of Pythagorean fuzzy graphs (PFGs) and Pythagorean fuzzy digraphs (PFDGs). Moreover, we derive the lower and upper bounds for the energy and Laplacian energy of PFGs. Finally, we present numerical examples, including the design of a satellite communication system and the evaluation of the schemes of reservoir operation to illustrate the applications of our proposed concepts in decision making.

scholarly journals Graphical Structures of Cubic Intuitionistic Fuzzy Information

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Sami Ullah Khan ◽  
Naeem Jan ◽  
Kifayat Ullah ◽  
Lazim Abdullah
Keyword(s):  
Decision Making ◽  
Future Study ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Graph ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Decision Making Problem ◽  
Intuitionistic Fuzzy Graphs ◽  
Interval Valued

The theory developed in this article is based on graphs of cubic intuitionistic fuzzy sets (CIFS) called cubic intuitionistic fuzzy graphs (CIFGs). This graph generalizes the structures of fuzzy graph (FG), intuitionistic fuzzy graph (IFG), and interval-valued fuzzy graph (IVFG). Moreover, several associated concepts are established for CIFG, such as the idea subgraphs, degree of CIFG, order of CIFG, complement of CIFG, path in CIFG, strong CIFG, and the concept of bridges for CIFGs. Furthermore, the generalization of CIFG is proved with the help of some remarks. In addition, the comparison among the existing and the proposed ideas is carried out. Finally, an application of CIFG in decision-making problem is studied, and some future study is proposed.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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 Certain Properties of Vague Graphs with a Novel Application

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1647
Author(s):  
Yongsheng Rao ◽  
Saeed Kosari ◽  
Zehui Shao
Keyword(s):  
Social Systems ◽  
Sufficient Conditions ◽  
Real Life ◽  
Laplacian Matrix ◽  
Fuzzy Graph ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Real World Problem ◽  
Laplacian Energy ◽  
Definition Of

Fuzzy graph models enjoy the ubiquity of being present in nature and man-made structures, such as the dynamic processes in physical, biological, and social systems. As a result of inconsistent and indeterminate information inherent in real-life problems that are often uncertain, for an expert, it is highly difficult to demonstrate those problems through a fuzzy graph. Resolving the uncertainty associated with the inconsistent and indeterminate information of any real-world problem can be done using a vague graph (VG), with which the fuzzy graphs may not generate satisfactory results. The limitations of past definitions in fuzzy graphs have led us to present new definitions in VGs. The objective of this paper is to present certain types of vague graphs (VGs), including strongly irregular (SI), strongly totally irregular (STI), neighborly edge irregular (NEI), and neighborly edge totally irregular vague graphs (NETIVGs), which are introduced for the first time here. Some remarkable properties associated with these new VGs were investigated, and necessary and sufficient conditions under which strongly irregular vague graphs (SIVGs) and highly irregular vague graphs (HIVGs) are equivalent were obtained. The relation among strongly, highly, and neighborly irregular vague graphs was established. A comparative study between NEI and NETIVGs was performed. Different examples are provided to evaluate the validity of the new definitions. A new definition of energy called the Laplacian energy (LE) is presented, and its calculation is shown with some examples. Likewise, we introduce the notions of the adjacency matrix (AM), degree matrix (DM), and Laplacian matrix (LM) of VGs. The lower and upper bounds for the Laplacian energy of a VG are derived. Furthermore, this study discusses the VG energy concept by providing a real-time example. Finally, an application of the proposed concepts is presented to find the most effective person in a hospital.

Designing DEMATEL method under bipolar fuzzy environment

2021 ◽  
pp. 1-17
Author(s):  
N. Deva ◽  
A. Felix
Keyword(s):  
Decision Making ◽  
Real Time ◽  
Structural Model ◽  
Mobile Network ◽  
Fuzzy Graph ◽  
Fuzzy Dematel ◽  
Fuzzy Environment ◽  
Competition Graph ◽  
Fuzzy Graphs ◽  
Bipolar Fuzzy Graphs

Bipolar fuzzy graph is more precise than a fuzzy graph when dealing with imprecision as it is focusing on the positive and negative information of each vertex and edge. Nowadays, researchers have utilized bipolar fuzzy graphs in decision-making problems. Bipolar fuzzy competition graphs aid to compute the competition between the vertices in bipolar fuzzy graphs. To depict the best competitions among the competitions of bipolar fuzzy graphs, the best bipolar fuzzy competition graph can be defined using bipolar fuzzy α-cut and the strength of the competition between the vertices can also be determined. Fuzzy graphs are used well to frame modelling in real-time problems. In particular, when the real-time scenario is modelled using the bipolar fuzzy graph, it gives more precision and flexibility. At present, researchers have focused on decision-making techniques with bipolar fuzzy graphs. The DEMATEL method is one of the powerful decision-making tools. It effectively analyses the complicated digraphs and matrices. The fuzzy DEMATEL technique can convert the interrelations between factors into an intelligible structural model of the system and divide them into cause and effect groups. Therefore, this study attempts to design the DEMATEL method under the bipolar fuzzy environment. To illustrate this proposed technique, the problem of identifying the best mobile network is taken. With this method, the benefits and drawbacks of networks are measured and a complicated bipolar fuzzy directed graph can be transformed into a viewed structure.

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