Aggregation Operators: Applications to Human Trafficking and Slavery

2018 ◽  
Vol 14 (03) ◽  
pp. 403-421
Author(s):  
John N. Mordeson ◽  
Sunil Mathew ◽  
Santanu Acharjee
Keyword(s):  
Human Trafficking ◽  
Aggregation Operators ◽  
Fuzzy Relations ◽  
Fuzzy Graphs ◽  
Application Methods ◽  
Theoretical Results

We introduce the idea of using aggregation operators to replace the concepts of minimum and maximum in the basic definitions and results involving fuzzy relations and fuzzy graphs. This development has begun with the replacement of minimum and maximum with [Formula: see text]-norms and [Formula: see text]-conorms, respectively. With this new theory, it will be possible to open the door to new theoretical results and at times more useful application methods. We apply our results in the areas of human trafficking and slavery.

Hamiltonian fuzzy graphs with application to human trafficking

2021 ◽  
Vol 550 ◽  
pp. 268-284
Author(s):  
Shanookha Ali ◽  
Sunil Mathew ◽  
J N Mordeson
Keyword(s):  
Human Trafficking ◽  
Fuzzy Graphs

Special Issue on Aggregation Operators and Clustering

2012 ◽  
Vol 16 (1) ◽  
pp. 147-147
Author(s):  
Vicenç Torra ◽  
Yasuo Narukawa ◽  
Mark Daumas
Keyword(s):  
Aggregation Operators ◽  
Kernel Functions ◽  
Trust Evaluation ◽  
Agglomerative Hierarchical Clustering ◽  
Special Issue ◽  
Pairwise Constraints ◽  
Journal Editors ◽  
Matrix Operations ◽  
Fuzzy Graphs ◽  
Quasiarithmetic Means

This issue features decision making and other tools used in artificial intelligence applications. More specifically, the issue includes five papers focused on aggregation operators and clustering. The series starts with a paper by Yoshida on weighted quasiarithmetic means that focuses on their monotonicity viewed from utility and weighting functions. In the second paper, Nohmi, Honda and Okazaki focus on trust evaluation for networks, studying matrix operations based on t-norms and t-conorms. The authors also propose fuzzy graphs using adjacent matrices. These works are followed by three on fuzzy clustering. Kanzawa, Endo and Miyamoto present a variation of fuzzy c-means based on kernel functions in an approach developed for data with tolerance. Endo covers clustering using kernel functions. The paper is based on a fuzzy nonmetric model including pairwise constraints in the clustering process. The concluding paper also uses pairwise constraints, but within agglomerative hierarchical clustering. Hamasuna, Endo and Miyamoto include clusterwise tolerance in their mode. As the editors of this issue, we would like to thank the referees for their work in the reviews and journal editors-in-chief Profs. Toshio Fukuda and Kaoru Hirota and the journal staff for their support.

scholarly journals Generalized Fuzzy Graph Connectivity Parameters with Application to Human Trafficking

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 424
Author(s):  
Arya Sebastian ◽  
John N Mordeson ◽  
Sunil Mathew
Keyword(s):  
Human Trafficking ◽  
Network Theory ◽  
Graph Connectivity ◽  
Fuzzy Graph ◽  
Graph Models ◽  
Edge Connectivity ◽  
Clustering Techniques ◽  
New Class ◽  
Large Size ◽  
Fuzzy Graphs

Graph models are fundamental in network theory. But normalization of weights are necessary to deal with large size networks like internet. Most of the research works available in the literature have been restricted to an algorithmic perspective alone. Not much have been studied theoretically on connectivity of normalized networks. Fuzzy graph theory answers to most of the problems in this area. Although the concept of connectivity in fuzzy graphs has been widely studied, one cannot find proper generalizations of connectivity parameters of unweighted graphs. Generalizations for some of the existing vertex and edge connectivity parameters in graphs are attempted in this article. New parameters are compared with the old ones and generalized values are calculated for some of the major classes like cycles and trees in fuzzy graphs. The existence of super fuzzy graphs with higher connectivity values are established for both old and new parameters. The new edge connectivity values for some wider classes of fuzzy graphs are also obtained. The generalizations bring substantial improvements in fuzzy graph clustering techniques and allow a smooth theoretical alignment. Apart from these, a new class of fuzzy graphs called generalized t-connected fuzzy graphs are studied. An algorithm for clustering the vertices of a fuzzy graph and an application related to human trafficking are also proposed.

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.

Properties of the aggregation operators related with fuzzy relations

2003 ◽  
Vol 139 (3) ◽  
pp. 615-633 ◽  
Author(s):  
Vania Peneva ◽  
Ivan Popchev
Keyword(s):  
Aggregation Operators ◽  
Fuzzy Relations

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.

Fuzzy Graphs Applied to Human Trafficking

2021 ◽  
pp. 99-120
Author(s):  
John N. Mordeson ◽  
Sunil Mathew ◽  
M. Binu
Keyword(s):  
Human Trafficking ◽  
Fuzzy Graphs
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