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In this chapter, we study the vulnerability of countries to climate change. We also examine the effects of climate change and the coronavirus on countries with respect to global hunger. We note that some models of the coronavirus can be placed in the setting of intuitionistic fuzzy mathematics.

We consider the interconnections between climate change and modern slavery. It is known that climate change can lead to extreme events which cause an increase in immigration and thus an increase in modern slavery and human trafficking. However, modern slavery activities may further perpetuate climate change and contribute to significant Greenhouse Gas emissions. We use the Guiasu method and the Dempster method to rank countries on their achievement pertinent to modern slavery.

We consider the risk of developed, emerging, and frontier market countries for their vulnerability to climate change. In study by A. Paun on climate change, 67 countries were ranked according their vulnerability. We place the findings into a mathematical framework using mathematics of uncertainty. We use techniques to rank the countries as to their risk. We use two fuzzy similarity measures to determine the similarity of the ranking methods.

We consider connectivity properties of fuzzy graphs. We introduce the notion of a container in a fuzzy graph. A container in a graph is a family of internally disjoint paths between a pair of vertices. A fuzzy container in a fuzzy graph is a family of internally disjoint strongest paths. We apply our results to examine connectivity properties with respect to human trafficking flow between regions in the world. We find the strength of connectedness between regions and fuzzy containers between them.

We continue our study of connectedness properties of fuzzy graphs. Generalizations for some existing vertex and edge connectivity in graphs are presented. New parameters are compared with older ones and generalized values are calculated for some of the major classes like cycles and trees in fuzzy graphs. We consider illegal human trafficking flow between 10 different subregions in the world.

The following is taken from [36]. The overwhelming majority of climate scientists agree that human activities, especially the burning of fossil fuels (coal, oil, and gas), are responsible for most of the climate change currently being observed. Scientists have been taking widespread measurements of Earth’s surface temperature since around 1880.

We turn our attention to the crimes of human trafficking and modern slavery. We rank countries with respect to their achievement of the SDGs pertinent to these crimes. We also use two fuzzy similarity measures to determine the similarity of the ranking methods.

In 2015, the leader of all the UN’s Member States agreed to the 2030 Agenda for Sustainable Development. The 17 Sustainable Development Goals and their 169 associated targets address five areas of critical importance: People, Planet, Prosperity, Peace, and Partnership. In this chapter we take the metrics and data provided in [68] and transform them into a fuzzy logic setting. We can then analyze the results in SDG Index and Dashboards Report 2019 by using techniques of fuzzy logic. Many of these 17 Sustainable Development Goals are related to the horrible crime of trafficking in persons. We also examine these goals in a fuzzy logic setting.

We compare the rankings of the countries in their achievement of the SDGs by using the similarity measures discussed in Chap. 1 and below in Sect. 6.2. We take the average of the three rankings using the AHP, Guiasu, and Yen method to determine one ranking. We also take the average of the three averages determined by the Stakeholder method to obtain one ranking. We then determine the ranking obtained in [68] for our third ranking. We make our comparisons in Sect. 6.3 of these three rankings. In Sect. 6.4, we compare the rankings of the countries with respect to human trafficking.

The reason for the choice of the SDGs in the table below was discussed in Chapter 3. However, we make some additional comments. Trafficking in persons disproportionately affects women and girls;\(71\%\) of all victims detected worldwide are female. The 2016 UNODC Global Report on Trafficking estimates that \(51\%\) of all detected trafficking victims are women and \(20\%\) are girls, [27].

We use mathematics of uncertainty to analyze the relationship between the sustainable development goals and human trafficking.

The purpose of this chapter is to rank the countries with respect to their achievement of the SDGs that are pertinent to modern slavery. We use the AHP-Guiasu-Yen method and the Stakeholder method to obtain the rankings.

Connectivity in fuzzy incidence graphs (FIG) is studied in this article. Different connectivity aspects of fuzzy incidence graphs such as bonding pair, doubly bonding pair and incidence cut of pairs are discussed. Incidence connectivity and incidence connectivity of pairs are introduced and results similar to Whitney’s Theorem are presented. The concept of t-connected fuzzy incidence graphs are also studied and some characterizations are obtained. An application related with illegal migration is presented. The most vulnerable routes in the Mexican-US border are focussed on and corresponding risks are evaluated using t-conorms.

Two major parameters associated with fuzzy graphs are discussed in this chapter. The first one, named as connectivity index gives an indication about the flow through the network and the second, called as Wiener index gives the average distance.

In this section, we introduce the concept of fuzzy geodetic convex sets and discuss some of their properties.

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.

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/whatishumantrafficking, United Nations Office on Drugs and Crime [6]).

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.

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

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.

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]).