دانلود کتاب ریاضیات فازی، نمودارها و مقیاس‌های شباهت

The world is faced with many serious challenges. In this book, we use mathematics of uncertainty to study these challenges. We consider the challenges human trafficking, cybersecurity, terrorism, mistreatment of women and children, space debris, and scamming. We provide Exercises and an instructor’s manual in case the book is used for a college course on global issues. In Chapter 1, we provide the notation and mathematical concepts needed for the book. The first part of the book rests heavily on fuzzy similarity measures.We provide the basis ideas of fuzzy similarity measures and fuzzy implication operators.We also lay the foundation to fuzzy graph theory, which is used to examine human trafficking and other global problems. In Chapter 2, we discuss how theoretical results from one family of fuzzy sets can be immediately carried over to another by the use of lattice isomorphisms. We show, however, that these families of fuzzy sets can arise natural in applications and that results of the application may not be carried over from one family to another. In Chapter 3, we consider cyber security.We determine fuzzy similarity measures of several issues with respect to country rankings. These issues include the risk to cyber crime. Statista collected data used in NordVPN’s analysis and approved the methodology used to create the Cyber Risk Index. In Chapter 4, we consider terrorism and bioterrorism. We examine the impact of terrorism and its effect on countries. We also find fuzzy similarity measures concerning issues related to terrorism and bioterrorism. We examine the relationship of Interpol global policy goals and sustainable development goals. In Chapter 5, we discuss how fuzzy implication operators can be used to determine fuzzy similarity measures involving the issues of health security and political risk. We also consider a country’s vulnerability and exposure to natural disaster. In Chapter 6, we once again use fuzzy similarity to examine country health issues. The Global Health Security Index has stated that all countries remain dangerously unprepared for future epidemic and pandemic threats. We use fuzzy implication operators as a basis of our study. For ease of reading, a small amount of results from Chapter 5 is repeated. In Chapter 7, we consider the mistreatment of women and children. There are many types of technology-facilitated violence. Studies confirm a high prevalence rate against women and girls. We study this situation using fuzzy implication operators. In Chapter 8, we consider space debris and sustainability. At the current rate of expansion, an environmental crisis in space will occur unless we act now.We consider issues involving sustainability and space. In particular, the connection between space debris and artificial intelligence is examined. In Chapter 9, we consider telecommunications. We provide the ranking of countries concerning issues of internet speed. We also consider the problem of spam and scam. Chapter 10 discusses two topological indices related with fuzzy graphs, namely eccentric connectivity index and modified eccentric connectivity index. Both indices are evaluated for most of the important fuzzy graph structures. An application of the index involving human trafficking chains is also presented. Chapter 11 deals with another fuzzy graph index known as neighborhood connectivity index, which can be used in quality of service problems and routing problems. This index is provided for a number of fuzzy graph structures. Neighborhood connectivity index of different types of products of fuzzy graphs is also discussed. In Chapter 12, we present sigma index and average sigma index of a fuzzy graph. A number of results evaluating these indices for different categories of fuzzy graphs and comparison of these indices with first and second Zagreb index are also provided. An algorithm for the computation of sigma index is given. A related application in the field of financing is discussed at the end. Chapter 13 gives another couple of indices namely Banhatti indices of first and second kind. Index values are obtained for paths, cycles, trees, complete fuzzy graphs, etc. Banhatti indices of graphs obtained by fuzzy graph operations are also discussed. Related algorithms and applications are also discussed. Chapter 14 presents a new type of connectivity parameter in fuzzy graphs called generalized cycle connectivity. In classical cycle connectivity, we use only strong cycles, whereas here every cycle is accounted. This will help us in the modeling of cyclic flow through various types of networks in a very different way. Most of the major fuzzy graph structures have been examined and their generalized cycle connectivity have been evaluated. Generalized cyclic cut vertices, bridges, generalized cyclic edge, and vertex connectivity are also discussed in detail. Cyclic stability and applications are also provided toward the end. Chapter 15 discusses another important fuzzy graph connectivity parameter called average fuzzy edge connectivity. We have presented the evaluation of average edge connectivity for most of the fuzzy graph classes. An application related to stress in youth is also provided.