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 A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 551 ◽  
Author(s):  
Liangsong Huang ◽  
Yu Hu ◽  
Yuxia Li ◽  
P. K. Kishore Kumar ◽  
Dipak Koley ◽  
...  
Keyword(s):  
Graph Theory ◽  
Optimization Problems ◽  
Real Life ◽  
Road Transport ◽  
Fuzzy Graph ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Real World Problem ◽  
Neutrosophic Graph ◽  
Definition Of

Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. The concepts of the regularity and degree of a node play a significant role in both the theory and application of graph theory in the neutrosophic environment. In this work, we describe the utility of the regular neutrosophic graph and bipartite neutrosophic graph to model an assignment problem, a road transport network, and a social network. For this purpose, we introduce the definitions of the regular neutrosophic graph, star neutrosophic graph, regular complete neutrosophic graph, complete bipartite neutrosophic graph, and regular strong neutrosophic graph. We define the d m - and t d m -degrees of a node in a regular neutrosophic graph. Depending on the degree of the node, this paper classifies the regularity of a neutrosophic graph into three types, namely d m -regular, t d m -regular, and m-highly irregular neutrosophic graphs. We present some theorems and properties of those regular neutrosophic graphs. The concept of an m-highly irregular neutrosophic graph on cycle and path graphs is also investigated in this paper. The definition of busy and free nodes in a regular neutrosophic graph is presented here. We introduce the idea of the μ -complement and h-morphism of a regular neutrosophic graph. Some properties of complement and isomorphic regular neutrosophic graphs are presented here.

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 Some Root Level Modifications in Interval Valued Fuzzy Graphs and Their Generalizations Including Neutrosophic Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 72 ◽  
Author(s):  
Naeem Jan ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Harish Garg ◽  
Bijan Davvaz ◽  
...  
Keyword(s):  
Decision Making ◽  
Essential Role ◽  
Real Life ◽  
Current Definition ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Decision Making Problem ◽  
Neutrosophic Graph ◽  
Definition Of ◽  
Interval Valued

Fuzzy graphs (FGs) and their generalizations have played an essential role in dealing with real-life problems involving uncertainties. The goal of this article is to show some serious flaws in the existing definitions of several root-level generalized FG structures with the help of some counterexamples. To achieve this, first, we aim to improve the existing definition for interval-valued FG, interval-valued intuitionistic FG and their complements, as these existing definitions are not well-defined; i.e., one can obtain some senseless intervals using the existing definitions. The limitations of the existing definitions and the validity of the new definitions are supported with some examples. It is also observed that the notion of a single-valued neutrosophic graph (SVNG) is not well-defined either. The consequences of the existing definition of SVNG are discussed with the help of examples. A new definition of SVNG is developed, and its improvement is demonstrated with some examples. The definition of an interval-valued neutrosophic graph is also modified due to the shortcomings in the current definition, and the validity of the new definition is proved. An application of proposed work is illustrated through a decision-making problem under the framework of SVNG, and its performance is compared with existing work.

scholarly journals An Introduction to Bipolar Single Valued Neutrosophic Graph Theory

2016 ◽  
Vol 841 ◽  
pp. 184-191 ◽  
Author(s):  
Said Broumi ◽  
Florentin Smarandache ◽  
Mohamed Talea ◽  
Assia Bakali
Keyword(s):  
Graph Theory ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Neutrosophic Graph ◽  
Intuitionistic Fuzzy Graphs ◽  
Bipolar Fuzzy Graphs

In this paper, we first define the concept of bipolar single neutrosophic graphs as the generalization of bipolar fuzzy graphs, N-graphs, intuitionistic fuzzy graph, single valued neutrosophic graphs and bipolar 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 COLLEGE STUDENT’S ERROR ANALYSIS BASED ON THEIR MATHEMATICAL CONNECTIONS ON GRAPH REPRESENTATION

2019 ◽  
Vol 4 (1) ◽  
pp. 18
Author(s):  
I ketut Suastika ◽  
Vivi Suwanti
Keyword(s):  
Graph Theory ◽  
College Student ◽  
Real Life ◽  
Graph Representation ◽  
High Ability ◽  
Pilot Studies ◽  
Graph Representations ◽  
Mathematical Connections ◽  
Life Problems ◽  
Basic Concepts

This study is investigates the college student’s errors on their graph representations making based on the mathematical connections indicators. Pilot studies were conducted with 4 college students of middle to high ability in Graph Theory class. Data analyze revealed that top 3 subject’s errors are 1) Finding the relations of a representations to it’s concepts and procedures, 2) Applying mathematics in other sciences or real life problems, and 3) Finding relations among procedures of the equivalent representations. Their lack of graph concepts understanding and it’s connections plays the major role in their errors. They failed at recognizing and choosing the suitable properties of graph which able to detect the error of their graph representation. So, in order to decrease college student errors in graph representations, we need to strengthen their basic concepts and its connections.

Dynamic Template Generation

2021 ◽  
pp. 1-37
Keyword(s):  
Optimization Problems ◽  
Real Life ◽  
Dynamic Test ◽  
Test Paper ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Life Problems ◽  
Conflicting Objectives ◽  
Complex Optimization ◽  
Dynamic Template

A test blueprint/test template, also known as the table of specifications, represents the structure of a test. It has been highly recommended in assessment textbook to carry out the preparation of a test with a test blueprint. This chapter focuses on modeling a dynamic test paper template using multi-objective optimization algorithm and makes use of the template in dynamic generation of examination test paper. Multi-objective optimization-based models are realistic models for many complex optimization problems. Modeling a dynamic test paper template, similar to many real-life problems, includes solving multiple conflicting objectives satisfying the template specifications.

Introduction

2021 ◽  
pp. 1-36
Author(s):  
Vadim Zverovich
Keyword(s):  
Graph Theory ◽  
Biological Networks ◽  
Real Life ◽  
Scale Free ◽  
Graph Theoretic ◽  
Life Problems ◽  
Scale Free Networks ◽  
Web Graph ◽  
The Web

This chapter gives a brief overview of selected applications of graph theory, many of which gave rise to the development of graph theory itself. A range of such applications extends from puzzles and games to serious scientific and real-life problems, thus illustrating the diversity of applications. The first section is devoted to the six earliest applications of graph theory. The next section introduces so-called scale-free networks, which include the web graph, social and biological networks. The last section describes a number of graph-theoretic algorithms, which can be used to tackle a number of interesting applications and problems of graph theory.

DE-PSO: A NEW HYBRID META-HEURISTIC FOR SOLVING GLOBAL OPTIMIZATION PROBLEMS

2011 ◽  
Vol 07 (03) ◽  
pp. 363-381 ◽  
Author(s):  
MILLIE PANT ◽  
RADHA THANGARAJ ◽  
AJITH ABRAHAM
Keyword(s):  
Global Optimization ◽  
Particle Swarm Optimization ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Real Life ◽  
Test Functions ◽  
Global Optimization Algorithm ◽  
Two Phase ◽  
Swarm Optimization ◽  
Life Problems

This paper presents a simple, hybrid two phase global optimization algorithm called DE-PSO for solving global optimization problems. DE-PSO consists of alternating phases of Differential Evolution (DE) and Particle Swarm Optimization (PSO). The algorithm is designed so as to preserve the strengths of both the algorithms. Empirical results show that the proposed DE-PSO is quite competent for solving the considered test functions as well as real life problems.

scholarly journals Optimization using evolutionary metaheuristic techniques: a brief review

2018 ◽  
Vol 15 (1) ◽  
pp. 44-53 ◽  
Author(s):  
Sajja Radhika ◽  
Aparna Chaparala
Keyword(s):  
Optimization Problems ◽  
Real Life ◽  
Multi Objective Optimization ◽  
Swarm Optimization ◽  
Multi Objective ◽  
Life Problems ◽  
Evolutionary Metaheuristic ◽  
Teaching Learning Based Optimization ◽  
Metaheuristic Techniques ◽  
Teaching Learning

Optimization is necessary for finding appropriate solutions to a range of real life problems. Evolutionary-approach-based meta-heuristics have gained prominence in recent years for solving Multi Objective Optimization Problems (MOOP). Multi Objective Evolutionary Approaches (MOEA) has substantial success across a variety of real-world engineering applications. The present paper attempts to provide a general overview of a few selected algorithms, including genetic algorithms, ant colony optimization, particle swarm optimization, and simulated annealing techniques. Additionally, the review is extended to present differential evolution and teaching-learning-based optimization. Few applications of the said algorithms are also presented. This review intends to serve as a reference for further work in this domain.

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