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.

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 q-Rung Orthopair Fuzzy Hypergraphs with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 260 ◽  
Author(s):  
Anam Luqman ◽  
Muhammad Akram ◽  
Ahmad N. Al-Kenani
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Research Study ◽  
Uncertain Data ◽  
Intuitionistic Fuzzy Sets ◽  
Uncertain Information ◽  
Pythagorean Fuzzy Sets ◽  
Proposed Model ◽  
Fuzzy Hypergraphs ◽  
New Framework

The concept of q-rung orthopair fuzzy sets generalizes the notions of intuitionistic fuzzy sets and Pythagorean fuzzy sets to describe complicated uncertain information more effectively. Their most dominant attribute is that the sum of the q th power of the truth-membership and the q th power of the falsity-membership must be equal to or less than one, so they can broaden the space of uncertain data. This set can adjust the range of indication of decision data by changing the parameter q, q ≥ 1 . In this research study, we design a new framework for handling uncertain data by means of the combinative theory of q-rung orthopair fuzzy sets and hypergraphs. We define q-rung orthopair fuzzy hypergraphs to achieve the advantages of both theories. Further, we propose certain novel concepts, including adjacent levels of q-rung orthopair fuzzy hypergraphs, ( α , β ) -level hypergraphs, transversals, and minimal transversals of q-rung orthopair fuzzy hypergraphs. We present a brief comparison of our proposed model with other existing theories. Moreover, we implement some interesting concepts of q-rung orthopair fuzzy hypergraphs for decision-making to prove the effectiveness of our proposed model.

scholarly journals Complex Intuitionistic Fuzzy Graphs with Application in Cellular Network Provider Companies

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 35 ◽  
Author(s):  
Naveed Yaqoob ◽  
Muhammad Gulistan ◽  
Seifedine Kadry ◽  
Hafiz Abdul Wahab
Keyword(s):  
Decision Making ◽  
Graph Theory ◽  
Fuzzy Sets ◽  
Cellular Network ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematical Approach ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Network Provider ◽  
Intuitionistic Fuzzy Graphs

In recent years, a mathematical approach of blending different aspects is on the way, which as a result gives a more generalized approach. Following the above mathematical approach, we combine two very powerful techniques, namely complex intuitionistic fuzzy sets and graph theory, and introduce the notion of complex intuitionistic fuzzy graphs. Then, we introduce certain notions including union, join and composition of complex intuitionistic fuzzy graphs, through which one can easily manipulate the complex intuitionistic fuzzy graphs in decision making problems. We elucidate these operations with some examples. We also describe the homomorphisms of complex intuitionistic fuzzy graphs. Finally, we provide an application in cellular network provider companies for the testing of our approach.

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 Towards Better Concordance among Contextualized Evaluations in FAST-GDM Problems

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 93
Author(s):  
Marcelo Loor ◽  
Ana Tapia-Rosero ◽  
Guy De Tré
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Heterogeneous Group ◽  
Intuitionistic Fuzzy ◽  
High Level ◽  
Consensus Reaching ◽  
Novel Algorithm

A flexible attribute-set group decision-making (FAST-GDM) problem consists in finding the most suitable option(s) out of the options under consideration, with a general agreement among a heterogeneous group of experts who can focus on different attributes to evaluate those options. An open challenge in FAST-GDM problems is to design consensus reaching processes (CRPs) by which the participants can perform evaluations with a high level of consensus. To address this challenge, a novel algorithm for reaching consensus is proposed in this paper. By means of the algorithm, called FAST-CR-XMIS, a participant can reconsider his/her evaluations after studying the most influential samples that have been shared by others through contextualized evaluations. Since exchanging those samples may make participants’ understandings more like each other, an increase of the level of consensus is expected. A simulation of a CRP where contextualized evaluations of newswire stories are characterized as augmented intuitionistic fuzzy sets (AIFS) shows how FAST-CR-XMIS can increase the level of consensus among the participants during the CRP.

Laplacian Energy of Digraphs and a Minimum Laplacian Energy Algorithm

2015 ◽  
Vol 26 (03) ◽  
pp. 367-380 ◽  
Author(s):  
Xingqin Qi ◽  
Edgar Fuller ◽  
Rong Luo ◽  
Guodong Guo ◽  
Cunquan Zhang
Keyword(s):  
Oriented Graph ◽  
Laplacian Matrix ◽  
Upper Bounds ◽  
Spectral Graph Theory ◽  
Extremal Graphs ◽  
Lower And Upper Bounds ◽  
Spectral Graph ◽  
Laplacian Energy ◽  
Energy Formula ◽  
Matrix Formula

In spectral graph theory, the Laplacian energy of undirected graphs has been studied extensively. However, there has been little work yet for digraphs. Recently, Perera and Mizoguchi (2010) introduced the directed Laplacian matrix [Formula: see text] and directed Laplacian energy [Formula: see text] using the second spectral moment of [Formula: see text] for a digraph [Formula: see text] with [Formula: see text] vertices, where [Formula: see text] is the diagonal out-degree matrix, and [Formula: see text] with [Formula: see text] whenever there is an arc [Formula: see text] from the vertex [Formula: see text] to the vertex [Formula: see text] and 0 otherwise. They studied the directed Laplacian energies of two special families of digraphs (simple digraphs and symmetric digraphs). In this paper, we extend the study of Laplacian energy for digraphs which allow both simple and symmetric arcs. We present lower and upper bounds for the Laplacian energy for such digraphs and also characterize the extremal graphs that attain the lower and upper bounds. We also present a polynomial algorithm to find an optimal orientation of a simple undirected graph such that the resulting oriented graph has the minimum Laplacian energy among all orientations. This solves an open problem proposed by Perera and Mizoguchi at 2010.

scholarly journals On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1485
Author(s):  
Pavel Sevastjanov ◽  
Ludmila Dymova ◽  
Krzysztof Kaczmarek
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Short Paper ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Methodological Problems ◽  
Shafer Theory ◽  
Sets Theory

In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.

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