scholarly journals Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Mamo Abebe Ashebo ◽  
V. N. Srinivasa Rao Repalle
Keyword(s):  
Optimization Problems ◽  
Real Life ◽  
Chromatic Polynomial ◽  
Fuzzy Graph ◽  
Traffic Light ◽  
Chromatic Polynomials ◽  
Combinatorial Optimization Problems ◽  
Fuzzy Graphs ◽  
Vertex Set ◽  
Fuzzy Vertex

Coloring of fuzzy graphs has many real life applications in combinatorial optimization problems like traffic light system, exam scheduling, register allocation, etc. In this paper, the concept of fuzzy chromatic polynomial of fuzzy graph is introduced and defined based on α-cuts of fuzzy graph. Two different types of fuzziness to fuzzy graph are considered in the paper. The first type was fuzzy graph with crisp vertex set and fuzzy edge set and the second type was fuzzy graph with fuzzy vertex set and fuzzy edge set. Depending on this, the fuzzy chromatic polynomials for some fuzzy graphs are discussed. Some interesting remarks on fuzzy chromatic polynomial of fuzzy graphs have been derived. Further, some results related to the concept are proved. Lastly, fuzzy chromatic polynomials for complete fuzzy graphs and fuzzy cycles are studied and some results are obtained.

scholarly journals 2-Quasitotal Fuzzy Graphs and Their Total Coloring

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
V. N. Srinivasa Rao Repalle ◽  
Fekadu Tesgera Agama
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Real Life ◽  
Register Allocation ◽  
Total Coloring ◽  
Fuzzy Graph ◽  
Traffic Light ◽  
Numerical Examples ◽  
Combinatorial Optimization Problems ◽  
Fuzzy Graphs

Coloring of fuzzy graphs has many real-life applications in combinatorial optimization problems like traffic light system, exam scheduling, and register allocation. The coloring of total fuzzy graphs and its applications are well studied. This manuscript discusses the description of 2-quasitotal graph for fuzzy graphs. The proposed concept of 2-quasitotal fuzzy graph is explicated by several numerical examples. Moreover, some theorems related to the properties of 2-quasitotal fuzzy graphs are stated and proved. The results of these theorems are compared with the results obtained from total fuzzy graphs and 1-quasitotal fuzzy graphs. Furthermore, it defines 2-quasitotal coloring of fuzzy total graphs and which is justified.

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 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 Flexible Wolf Pack Algorithm for Dynamic Multidimensional Knapsack Problems

Research ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Husheng Wu ◽  
Renbin Xiao
Keyword(s):  
Dynamic Optimization ◽  
Optimization Problems ◽  
Real Life ◽  
Dynamic Environment ◽  
Combinatorial Problem ◽  
Knapsack Problems ◽  
Dynamic Optimization Problems ◽  
Practical Applications ◽  
Combinatorial Optimization Problems ◽  
Multidimensional Knapsack

Optimization problems especially in a dynamic environment is a hot research area that has attracted notable attention in the past decades. It is clear from the dynamic optimization literatures that most of the efforts have been devoted to continuous dynamic optimization problems although the majority of the real-life problems are combinatorial. Moreover, many algorithms shown to be successful in stationary combinatorial optimization problems commonly have mediocre performance in a dynamic environment. In this study, based on binary wolf pack algorithm (BWPA), combining with flexible population updating strategy, a flexible binary wolf pack algorithm (FWPA) is proposed. Then, FWPA is used to solve a set of static multidimensional knapsack benchmarks and several dynamic multidimensional knapsack problems, which have numerous practical applications. To the best of our knowledge, this paper constitutes the first study on the performance of WPA on a dynamic combinatorial problem. By comparing two state-of-the-art algorithms with the basic BWPA, the simulation experimental results demonstrate that FWPA can be considered as a feasibility and competitive algorithm for dynamic optimization problems.

scholarly journals Quantum Inspired General Variable Neighborhood Search (qGVNS) for Dynamic Garbage Collection

2017 ◽  
Author(s):  
Christos Papalitsas ◽  
Panayiotis Karakostas ◽  
Theodore Andronikos ◽  
Spyros Sioutas ◽  
Konstantinos Giannakis
Keyword(s):  
Variable Neighborhood Search ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Real Life ◽  
Neighborhood Search ◽  
Np Hard ◽  
Combinatorial Optimization Problems ◽  
Np Hard Problem ◽  
Gps System ◽  
Tools And Techniques

General Variable Neighborhood Search (GVNS) is a well known and widely used metaheuristic for efficiently solving many NP-hard combinatorial optimization problems. Quantum General Variable Neighborhood Search (qGVNS) is a novel, quantum inspired extension of the conventional GVNS. Its quantum nature derives from the fact that it takes advantage and incorporates tools and techniques from the field of quantum computation. Travelling Salesman Problem (TSP) is a well known NP-Hard problem which has broadly been used for modelling many real life routing cases. As a consequence, TSP can be used as a basis for modelling and finding routes for Geographical Systems (GPS). In this paper, we examine the potential use of this method for the GPS system of garbage trucks. Specifically, we provide a thorough presentation of our method accompanied with extensive computational results. The experimental data accumulated on a plethora of symmetric TSP instances (symmetric in order to faithfully simulate GPS problems), which are shown in a series of figures and tables, allow us to conclude that the novel qGVNS algorithm can provide an efficient solution for this type of geographical problems.

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 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.

Vertex Connectivity of Fuzzy Graphs with Applications to Human Trafficking

2018 ◽  
Vol 14 (03) ◽  
pp. 457-485 ◽  
Author(s):  
Shanookha Ali ◽  
Sunil Mathew ◽  
John N. Mordeson ◽  
Hossein Rashmanlou
Keyword(s):  
Real Number ◽  
Human Trafficking ◽  
Dynamic Network ◽  
Arbitrary Real Number ◽  
Fuzzy Graph ◽  
Vertex Connectivity ◽  
The Past ◽  
Fuzzy Graphs ◽  
Number Formula ◽  
Fuzzy Vertex

Connectivity is the most important aspect of a dynamic network. It has been widely studied and applied in different perspectives in the past. In this paper, constructions of [Formula: see text]-connected fuzzy graphs for an arbitrary real number [Formula: see text] and average fuzzy vertex connectivity of fuzzy graphs are discussed. Average fuzzy vertex connectivity of fuzzy trees, fuzzy cycles and complete fuzzy graphs are studied. The concept of a uniformly [Formula: see text]-connected fuzzy graph is introduced and characterized towards the end. An application related to human trafficking is also discussed.

scholarly journals Stability concepts in bargaining games

2021 ◽  
Author(s):  
Somnath Kundu
Keyword(s):  
Combinatorial Optimization ◽  
Cost Sharing ◽  
Optimization Problems ◽  
Real Life ◽  
Profit Sharing ◽  
Bargaining Games ◽  
Bargaining Process ◽  
Combinatorial Optimization Problems ◽  
Definition Of ◽  
Stability Concepts

In this thesis we discuss some novel concepts of stability in bargaining games, over a network setting. So far, the studies on bargaining games were done as profit sharing problems, whose underlying combinatorial optimization problems are of packing type. In our work, we study bargaining games from a cost sharing perspective, where the underlying combinatorial optimization problems are covering type problems. Unlike previous studies, where bargaining processes are restricted to only two players, we study bargaining games over a more generic hypergraph setting, which allows any bargaining process to be formed among any number of players. In previous studies of bargaining games, the objects that are being negotiated are assumed to be uniform and only the outcomes of the negotiations are allowed to be different. However, in our study, we accommodate possibilities of non-uniform weights of the objects that are being negotiated, which is closer to any real life scenario. Finally we extend our study to incorporate socially aware players by introducing a relaxed and innovative definition of stability.

Sign in / Sign up

Export Citation Format

Share Document