scholarly journals Revision of Pseudo-Ultrametric Spaces Based on m-Polar T-Equivalences and Its Application in Decision Making

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1232
Author(s):  
Azadeh Zahedi Khameneh ◽  
Adem Kilicman ◽  
Fadzilah Md Ali
Keyword(s):  
Metric Spaces ◽  
Cartesian Product ◽  
Equivalence Relations ◽  
Fuzzy Graph ◽  
Triangular Norm ◽  
Ultrametric Spaces ◽  
Fuzzy Environment ◽  
Fuzzy Similarity ◽  
Fuzzy Graphs ◽  
New Type

In mathematics, distance and similarity are known as dual concepts. However, the concept of similarity is interpreted as fuzzy similarity or T-equivalence relation, where T is a triangular norm (t-norm in brief), when we discuss a fuzzy environment. Dealing with multi-polarity in practical examples with fuzzy data leadsus to introduce a new concept called m-polar T-equivalence relations based on a finitely multivalued t-norm T, and to study the metric behavior of such relations. First, we study the new operators including the m-polar triangular norm T and conorm S as well as m-polar implication I and m-polar negation N, acting on the Cartesian product of [0,1]m-times.Then, using the m-polar negations N, we provide a method to construct a new type of metric spaces, called m-polar S-pseudo-ultrametric, from the m-polar T-equivalences, and reciprocally for constructing m-polar T-equivalences based on the m-polar S-pseudo-ultrametrics. Finally, the link between fuzzy graphs and m-polar S-pseudo-ultrametrics is considered. An algorithm is designed to plot a fuzzy graph based on the m-polar SL-pseudo-ultrametric, where SL is the m-polar Lukasiewicz t-conorm, and is illustrated by a numerical example which verifies our method.

scholarly journals Multiple Attribute Decision-Making Problem Using Picture Fuzzy Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Sk. Amanathulla ◽  
G. Muhiuddin ◽  
D. Al-Kadi ◽  
M. Pal
Keyword(s):  
Decision Making ◽  
Cartesian Product ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Environment ◽  
Fuzzy Graphs ◽  
Determination Process ◽  
Multiple Attribute ◽  
Picture Fuzzy Set ◽  
Almost All ◽  
The Relationship

In a picture fuzzy environment, almost all multiple attribute decision-making ( MADM ) methods have been discussed a type of problem in which there is no relationship among the attributes. Although the relationship among the attributes should be considered in the actual applications, so we need to pay attention to that important issue. This article applied graph theory to the picture fuzzy set ( PFS ) and obtained a new method, MADM , to solve complicated problems under a picture fuzzy environment. The developed method can capture the relationship among the attributes that cannot be handled well by any existing methods. This study introduces union, intersection, sum, Cartesian product, the composition of picture fuzzy graphs ( PFG s), and their important properties. Finally, by considering the importance of relationships among attributes in the determination process, two algorithms, based on PFG , have developed to solve complicated problems using picture fuzzy information. Also, two numerical examples have introduced to explain how to deal with the MADM problem under picture fuzzy environment.

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.

scholarly journals Dominating Energy of Operations on Intuitionistic Fuzzy Graphs

2018 ◽  
Vol 7 (4.10) ◽  
pp. 328 ◽  
Author(s):  
A. Kalimulla ◽  
R. Vijayaragavan ◽  
S. Sharief Basha
Keyword(s):  
Cartesian Product ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Intuitionistic Fuzzy Graphs

The concept of energy of an Intuitionistic Fuzzy Graph is extended to dominating Energy in operations on Intuitionistic Fuzzy Graph. In this paper, We have obtained the value of dominating Energy in different operations such as complement, Union, Join, Cartesian product and composition between two intuitionistic Fuzzy graphs. Also we study the relation between the dominating Energy in the operations on two Intuitionistic Fuzzy Graphs.  

First Zagreb index on a fuzzy graph and its application

2021 ◽  
pp. 1-13
Author(s):  
Sk Rabiul Islam ◽  
Madhumangal Pal
Keyword(s):  
Network Theory ◽  
Cartesian Product ◽  
Spectral Graph Theory ◽  
Fuzzy Graph ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Molecular Chemistry ◽  
Spectral Graph ◽  
Fuzzy Graphs ◽  
A Company

The Zagreb index (ZI) is a very important graph parameter and it is extensively used in molecular chemistry, spectral graph theory, network theory and several fields of mathematics and chemistry. In this article, the first ZI is studied for several fuzzy graphs like path, cycle, star, fuzzy subgraph, etc. and presented an ample number of results. Also, it is established that the complete fuzzy graph has maximal first ZI among n-vertex fuzzy graphs. Some bounds of first ZI are discussed for Cartesian product, composition, union and join of two fuzzy graphs. An algorithm has been designed to calculate the first ZI of a fuzzy graph. At the end of the article, a multi-criteria decision making (MCDM) method is provided using the first ZI of a fuzzy graph to find the best employee in a company. Also a comparison is provided among related indices on the result of application and shown that our method gives better results.

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.

Inverse Fuzzy Graphs with Applications

2020 ◽  
Vol 16 (02) ◽  
pp. 397-418
Author(s):  
R. A. Borzooei ◽  
R. Almallah ◽  
Y. B. Jun ◽  
H. Ghaznavi
Keyword(s):  
New York ◽  
Fuzzy Sets ◽  
Real Life ◽  
Academic Press ◽  
Membership Degree ◽  
Fuzzy Relations ◽  
Fuzzy Graph ◽  
The Real ◽  
Fuzzy Graphs ◽  
New Type

Rosenfeld [A. Rosenfeld, Fuzzy Graphs, Fuzzy Sets and Their Applications, eds. L. A. Zadeh, K. S. Fu and M. Shimura (Academic Press, New York, 1975), pp. 77–95.] defined the fuzzy relations on the fuzzy sets and developed the structure of fuzzy graph, as a graph with a membership degree (between zero and one) for the vertices and edges such that the membership degree of every edge is less than or equal to the minimum of the membership degree of its endpoints. Although this model of graph has many applications in the real life, it fails to solve a lot of problems, which we can use graph for its representation. This paper aimed to demonstrate a new type of graph with a membership degree (between zero and one) for the vertices and edges so that the membership degree of every edge becomes more than or equals the minimum of the membership degrees of its endpoints. This new type of graph is called inverse fuzzy graph “or” I-fuzzy graph, which can play a role in solving many problems which are not solved by fuzzy graph.

scholarly journals Decision Making Approach under Pythagorean Dombi Fuzzy Graphs for Selection of Leading Textile Industry

2019 ◽  
Vol 24 (4) ◽  
pp. 102
Author(s):  
Muhammad Akram ◽  
Jawaria Mohsan Dar ◽  
Sundas Shahzadi
Keyword(s):  
Decision Making ◽  
Textile Industry ◽  
Research Study ◽  
Cartesian Product ◽  
Multi Criteria Decision Making ◽  
Fuzzy Graph ◽  
Operational Parameter ◽  
Strong Product ◽  
Fuzzy Graphs ◽  
Selection Of

Graphs play a pivotal role in structuring real-world scenarios such as network security and expert systems. Numerous extensions of graph theoretical conceptions have been established for modeling uncertainty in graphical network situations. The Pythagorean Dombi fuzzy graph (PDFG), a generalization of the fuzzy Dombi graph (FDG), is very useful in representing vague relations between several objects, whereas the operational parameter has a flexible nature in decision-making problems. The main objective of this research study is to expand the area of discussion on PDFGs by establishing fruitful results and notions related to operations such as the direct product, Cartesian product, semi-strong product, strong product, and composition on PDFGs. Certain concepts, including the degree of vertices and total degree, are discussed as its modifications. Meanwhile, these outcomes are considered on PDFGs maintaining the strongness property. At the end, an algorithm for Pythagorean Dombi fuzzy multi-criteria decision-making is given, and a numerical example based on the selection of a leading textile industry is put forward to clarify the suitability of the proposed approach.

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 Signless Laplacian Energy in Products of Intuitionistic Fuzzy Graphs

2019 ◽  
Vol 8 (3) ◽  
pp. 8536-8545
Keyword(s):  
Tensor Product ◽  
Cartesian Product ◽  
Fuzzy Graph ◽  
Lexicographic Product ◽  
Intuitionistic Fuzzy ◽  
Strong Product ◽  
Fuzzy Graphs ◽  
Laplacian Energy ◽  
Signless Laplacian ◽  
Intuitionistic Fuzzy Graphs

The observation of an Intuitionistic Fuzzy Graph’s signless laplacian energy is expanded innumerous products in Intuitionistic Fuzzy Graph. During this paper, we have got the value of signless laplacian Energy in unrelated products such as Cartesian product, Lexicographic Product, Tensor product and Strong Product, product, product and product amongst 2 intuitionistic Fuzzy graphs. Additionally we tend to study the relation between the Signless laplacian Energy within the varied products in 2 Intuitionistic Fuzzy Graphs

scholarly journals Some new fixed point theorems for contractive and nonexpansive mappings

Filomat ◽  
2014 ◽  
Vol 28 (2) ◽  
pp. 313-317 ◽  
Author(s):  
Rajendra Pant
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Vector Spaces ◽  
Ultrametric Spaces ◽  
Nonlinear Anal ◽  
New Type

In the present paper, we obtain some new fixed point theorems for set-valued contractive and nonexpansive mappings in the setting of ultrametric spaces. Our theorems complement, generalize and extend some well known results of Petalas and Vidalis [A fixed point theorem in non-Archimedean vector spaces, Proc. Amer. Math. Soc 118(1993), 819-821.], Suzuki [A new type of fixed point theorem in metric spaces, Nonlinear Anal. 71(2009), 5313-5317.] and others.

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