scholarly journals Clustering algorithm with strength of connectedness for $ m $-polar fuzzy network models

2021 ◽  
Vol 19 (1) ◽  
pp. 420-455
Author(s):  
Muhammad Akram ◽  
◽  
Saba Siddique ◽  
Majed G. Alharbi ◽  
Keyword(s):  
Clustering Algorithm ◽  
Research Study ◽  
Research Work ◽  
Network Models ◽  
Uncertain Information ◽  
Fuzzy Graph ◽  
Clustering Method ◽  
Fuzzy Graphs ◽  
Degree Of A Vertex ◽  
Fuzzy Network

<abstract><p>In this research study, we first define the strong degree of a vertex in an $ m $-polar fuzzy graph. Then we present various useful properties and prove some results concerning this new concept, in the case of complete $ m $-polar fuzzy graphs. Further, we introduce the concept of $ m $-polar fuzzy strength sequence of vertices, and we also investigate it in the particular instance of complete $ m $-polar fuzzy graphs. We discuss connectivity parameters in $ m $-polar fuzzy graphs with precise examples, and we investigate the $ m $-polar fuzzy analogue of Whitney's theorem. Furthermore, we present a clustering method for vertices in an $ m $-polar fuzzy graph based on the strength of connectedness between pairs of vertices. In order to formulate this method, we introduce terminologies such as $ \epsilon_A $-reachable vertices in $ m $-polar fuzzy graphs, $ \epsilon_A $-connected $ m $-polar fuzzy graphs, or $ \epsilon_A $-connected $ m $-polar fuzzy subgraphs (in case the $ m $-polar fuzzy graph itself is not $ \epsilon_A $-connected). Moreover, we discuss an application for clustering different companies in consideration of their multi-polar uncertain information. We then provide an algorithm to clearly understand the clustering methodology that we use in our application. Finally, we present a comparative analysis of our research work with existing techniques to prove its applicability and effectiveness.</p></abstract>

scholarly journals Degree based models of granular computing under fuzzy indiscernibility relations

2021 ◽  
Vol 18 (6) ◽  
pp. 8415-8443
Author(s):  
Muhammad Akram ◽  
◽  
Ahmad N. Al-Kenani ◽  
Anam Luqman ◽  
Keyword(s):  
Granular Computing ◽  
Research Work ◽  
Real Life ◽  
Network Models ◽  
Uncertain Information ◽  
Fuzzy Information ◽  
Graph Models ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Real Life Data

<abstract><p>The aim of this research work is to put forward fuzzy models of granular computing based on fuzzy relation and fuzzy indiscernibility relation. Thanks to fuzzy information granulation to provide multi-level visualization of problems that include uncertain information. In such a granulation, fuzzy sets and fuzzy graphs help us to represent relationships among granules, groups or clusters. We consider the fuzzy indiscernibility relation of a fuzzy knowledge representation system ($ \mathcal{I} $). We describe the granular structures of $ \mathcal{I} $, including discernibility, core, reduct and essentiality of $ \mathcal{I} $. Then we examine the contribution of these structures to granular computing. Moreover, we introduce certain granular structures using fuzzy graph models and discuss degree based model of fuzzy granular structures. Granulation of network models based on fuzzy information effectively handles real life data which possesses uncertainty and vagueness. Finally, certain algorithms of proposed models are developed and implemented to solve real life problems involving uncertain granularities. We also present a concise comparison of the models developed in our work with other existing methodologies.</p></abstract>

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.

Recent Developments on the Basics of Fuzzy Graph Theory

2020 ◽  
pp. 419-436 ◽  
Author(s):  
Ganesh Ghorai ◽  
Kavikumar Jacob
Keyword(s):  
Graph Theory ◽  
Planar Graphs ◽  
Fuzzy Graph ◽  
Threshold Graphs ◽  
Fuzzy Graphs ◽  
Degree Of A Vertex ◽  
Recent Developments

In this chapter, the authors introduce some basic definitions related to fuzzy graphs like directed and undirected fuzzy graph, walk, path and circuit of a fuzzy graph, complete and strong fuzzy graph, bipartite fuzzy graph, degree of a vertex in fuzzy graphs, fuzzy subgraph, etc. These concepts are illustrated with some examples. The recently developed concepts like fuzzy planar graphs are discussed where the crossing of two edges are considered. Finally, the concepts of fuzzy threshold graphs and fuzzy competitions graphs are also given as a generalization of threshold and competition graphs.

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.

scholarly journals Dengue Disease Detection using K- Means, Hierarchical, Kohonen- SOM Clustering

2019 ◽  
Vol 8 (10) ◽  
pp. 904-907
Keyword(s):  
Data Mining ◽  
Clustering Algorithm ◽  
Research Work ◽  
Data Mining Algorithm ◽  
Clustering Method ◽  
Dengue Disease ◽  
Related Data ◽  
Som Algorithm ◽  
Som Clustering ◽  
Kohonen Som

Data Mining is the process of extracting useful information. Data Mining is about finding new information from pre-existing databases. It is the procedure of mining facts from data and deals with the kind of patterns that can be mined. Therefore, this proposed work is to detect and categorize the illness of people who are affected by Dengue through Data Mining techniques mainly as the Clustering method. Clustering is the method of finding related groups of data in a dataset and used to split the related data into a group of sub-classes. So, in this research work clustering method is used to categorize the age group of people those who are affected by mosquito-borne viral infection using K-Means and Hierarchical Clustering algorithm and Kohonen-SOM algorithm has been implemented in Tanagra tool. The scientists use the data mining algorithm for preventing and defending different diseases like Dengue disease. This paper helps to apply the algorithm for clustering of Dengue fever in Tanagra tool to detect the best results from those algorithms.

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.

Menger’s theorem for m-polar fuzzy graphs and application of m-polar fuzzy edges to road network

2021 ◽  
pp. 1-22
Author(s):  
Muhammad Akram ◽  
Saba Siddique ◽  
Uzma Ahmad
Keyword(s):  
Road Network ◽  
Research Work ◽  
Basic Structure ◽  
Fuzzy Graph ◽  
Research Article ◽  
Cut Vertex ◽  
Fuzzy Graphs ◽  
Menger's Theorem ◽  
Different Types ◽  
The Difference

The main objective of this research article is to classify different types of m-polar fuzzy edges in an m-polar fuzzy graph by using the strength of connectedness between pairs of vertices. The identification of types of m-polar fuzzy edges, including α-strong m-polar fuzzy edges, β-strong m-polar fuzzy edges and δ-weak m-polar fuzzy edges proved to be very useful to completely determine the basic structure of m-polar fuzzy graph. We analyze types of m-polar fuzzy edges in strongest m-polar fuzzy path and m-polar fuzzy cycle. Further, we define various terms, including m-polar fuzzy cut-vertex, m-polar fuzzy bridge, strength reducing set of vertices and strength reducing set of edges. We highlight the difference between edge disjoint m-polar fuzzy path and internally disjoint m-polar fuzzy path from one vertex to another vertex in an m-polar fuzzy graph. We define strong size of an m-polar fuzzy graph. We then present the most celebrated result due to Karl Menger for m-polar fuzzy graphs and illustrate the vertex version of Menger’s theorem to find out the strongest m-polar fuzzy paths between affected and non-affected cities of a country due to an earthquake. Moreover, we discuss an application of types of m-polar fuzzy edges to determine traffic-accidental zones in a road network. Finally, a comparative analysis of our research work with existing techniques is presented to prove its applicability and effectiveness.

t-Norm Fuzzy Graphs

2018 ◽  
Vol 14 (01) ◽  
pp. 129-143 ◽  
Author(s):  
John N. Mordeson ◽  
Sunil Mathew
Keyword(s):  
Connectivity Index ◽  
The Other ◽  
Fuzzy Graph ◽  
Trafficking In Persons ◽  
High Susceptibility ◽  
Fuzzy Graphs ◽  
High Connectivity ◽  
The Government ◽  
Definition Of ◽  
Fuzzy Network

We generalize the definition of a fuzzy graph by replacing minimum in the basic definitions with an arbitrary [Formula: see text]-norm. The reason for this is that some applications are better modeled with a [Formula: see text]-norm other than minimum. We develop a measure on the susceptibility of trafficking in persons for networks by using a [Formula: see text]-norm other than minimum. We also develop a connectivity index for a fuzzy network. In one application, a high connectivity index means a high susceptibility to trafficking. In the other application, we use a method called the eccentricity of an origin country to determine the susceptibility of a network to trafficking in persons. The models rest on the vulnerabilities and the government responses of countries to trafficking.

scholarly journals Complete Regular Fuzzy Graphs

2019 ◽  
Vol 8 (3S3) ◽  
pp. 25-29
Keyword(s):  
Fuzzy Graph ◽  
Induced Subgraph ◽  
Fuzzy Graphs ◽  
Degree Of A Vertex ◽  
The Given ◽  
Regular Property

In this paper, some properties of complete degree and complete regular fuzzy graphs are discussed. They are illustrated through various examples. It is proved that every fuzzy graph is an induced subgraph of a complete regular fuzzy graph. The procedure described in the proof is illustrated through an example. Also the complete degree of a vertex in fuzzy graphsformed by the operation Union in terms of the complete degree of vertices in the given fuzzy graphs for some particular cases are obtained. Using them, their complete regular property is studied.

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