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2018 | Book

Fuzzy Graph Theory with Applications to Human Trafficking

Authors: Prof. Dr. John N. Mordeson, Prof. Dr. Sunil Mathew, Prof. Dr. Davender S. Malik

Publisher: Springer International Publishing

Book Series : Studies in Fuzziness and Soft Computing

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About this book

This book reports on advanced concepts in fuzzy graph theory, showing a set of tools that can be successfully applied to understanding and modeling illegal human trafficking. Building on the previous book on fuzzy graph by the same authors, which set the fundamentals for readers to understand this developing field of research, this second book gives a special emphasis to applications of the theory. For this, authors introduce new concepts, such as intuitionistic fuzzy graphs, the concept of independence and domination in fuzzy graphs, as well as directed fuzzy networks, incidence graphs and many more.

Table of Contents

Frontmatter
Chapter 1. Strengthening and Weakening Members of a Network
Abstract
In 1965, Lotfi A. Zadeh (Fuzzy sets. Inf. Control 8, 338–353, 1965) [34] introduced a new type of set called a fuzzy set and a new logic later known as fuzzy logic. Instead of YES or NO, regarding the existence of an element in a set, he used the degree of membership, which allows an element to exist in a set with a partial grade of membership. The applications of fuzzy logic are profound and widespread.
John N. Mordeson, Sunil Mathew, Davender S. Malik
Chapter 2. Domination in Fuzzy Graphs
Abstract
The results of the next two sections are based on Somasundaram, Somasundaram (Pattern Recongit Lett 19:787–791, 1998), [29]. The formal mathematical definition of domination was given by Ore, (Theory of graphs. American Mathematical Society, Providence, 1962), [22]. Cockayne and Hedetnieme, (Networks 7:247–261, 1977, [3]), published a survey paper on this topic in 1977 and since then hundreds of papers have been published on this subject. According to Somasundaram, Somasundaram (Pattern Recongit Lett 19:787–791, 1998, [29]), the rapid growth of research in this area is due to the following three factors. (1) The diversity of applications of domination theory to both real world and mathematical coverings or location problems. (2) The wide variety of domination parameters that can be defined. (3) The NP-completeness of the basic domination problem, its close and natural relationship to other NP-complete problems and the subsequent interest in finding polynomial time solutions to domination problems in special classes of graphs.
John N. Mordeson, Sunil Mathew, Davender S. Malik
Chapter 3. Fuzzy Incidence Graphs
Abstract
We introduce the notion of the degree of incidence of a vertex and an edge in a fuzzy graph in fuzzy graph theory. We concentrate on incidence, where the edge is adjacent to the vertex. We determine results concerning bridges, cutvertices, cutpairs, fuzzy incidence paths, fuzzy incidence tree for fuzzy incidence graphs. In (Dinesh, Ph.D. thesis, Kannur University, Kerala, India, [4]; Dinesh, Adv Fuzzy Sets Syst, 21:33–48, 2016, [5]), Dinesh introduced the notion of the degree of incidence of a vertex and an edge in fuzzy graph theory. This notion seem to have potential use in a variety of areas involving networks, Mordeson (Adv Fuzzy Sets Syst, 22:121–133, 2016, [12]).
John N. Mordeson, Sunil Mathew, Davender S. Malik
Chapter 4. Networks
Abstract
In the first three sections, we devote our attention to the problem of maximizing the flow through a network. We present a fuzzy version of a max flow, min cut theorem.
John N. Mordeson, Sunil Mathew, Davender S. Malik
Chapter 5. Complementary Fuzzy Incidence Graphs
Abstract
Recall that if x is a member of a set X and \(t\in [0,1],\) then we define the fuzzy subset \(x_{t}\) of X by \(x_{t}(x)=t\) and \(x_{t}(y)=0\) for all \(y\in X\backslash \{x\}.\) We call \(x_{t}\) a fuzzy singleton
John N. Mordeson, Sunil Mathew, Davender S. Malik
Chapter 6. Human Trafficking: Source, Transit, Destination Designations
Abstract
Trafficking in persons has been defined as the recruitment, transportation, transfer, harboring or receipt of persons by means of threat or use of force or other forms of coercion, of abduction, of fraud, of deception, of the abuse of power or of a position of vulnerability or the giving or receiving of payments or benefits to achieve the consent of a person having control over another person, for the purpose of exploitation (http://​www.​unodc.​org/​unodc/​en/​human-trafficking/​whatishumantraff​icking, United Nations Office on Drugs and Crime [6]).
John N. Mordeson, Sunil Mathew, Davender S. Malik
Chapter 7. Human Trafficking: Policy Intervention
Abstract
In Lutz and Lotspeich, Prot Proj J Hum Rights Civ Soc 2:124–199, 2009, [8], causal linkages between commercial sex and human trafficking were examined. It was determined that a three-link chain of necessary conditions existed: a population vulnerable to trafficking, a capable trafficking organization, and a sex market, was identified. All three links are required for trafficking into commercial sex. Thus, trafficking can be examined by policy intervention at any link. Prospects for policy success at the three points of intervention were compared. It was shown in Lutz and Lotspeich, Prot Proj J Hum Rights Civ Soc 2:124–199, 2009, [8] that a strategy of suppressing sex markets is least likely to be successful in reducing human trafficking.
John N. Mordeson, Sunil Mathew, Davender S. Malik
Backmatter
Metadata
Title
Fuzzy Graph Theory with Applications to Human Trafficking
Authors
Prof. Dr. John N. Mordeson
Prof. Dr. Sunil Mathew
Prof. Dr. Davender S. Malik
Copyright Year
2018
Electronic ISBN
978-3-319-76454-2
Print ISBN
978-3-319-76453-5
DOI
https://doi.org/10.1007/978-3-319-76454-2

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