Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Sustainable Development Goals and Homelessness

The United Nation's Sustainable Development Goals encourage countries to solve many social problems‎. ‎One of these problems is homelessness‎. ‎We consider those goals which are most pertinent to homelessness according to \cite{13}‎. ‎We rank countries with respect to the‎  achievement of these goals‎. ‎We use fuzzy similarity measures to determine‎ ‎ the degree of similarity between these rankings‎. ‎We use three methods to‎ ‎ rank the counties‎, ‎namely‎, ‎the Analytic Hierarchy Process‎, ‎the Guiasu‎ ‎ method,‎ ‎and the Yen method‎. ‎Overall scores of categories in some basic‎ ‎ research papers pertaining to Sustainable Development Goals were obtained by‎ ‎ using multiplication of the scores of the category's targets‎. ‎Multiplication‎ ‎ was used to agree with the philosophy that in order for a high score to be‎ ‎ obtained,‎ ‎all targets must have a high score‎. ‎To support this philosophy in‎ ‎ the decision process‎, ‎we use the $t$-norms bounded difference‎, ‎algebraic‎ ‎ product,‎ ‎and standard intersection as experts‎. ‎We also suggest a way the‎ ‎ techniques used here can be extended to nonstandard analysis‎

Assessing policy stability in Iraq: a fuzzy approach to modeling preferences

The first Council of Representatives elected under the new Iraqi Constitution was unable to pass legislation required to achieve the political benchmarks set by the government. We argue that the exercise of a qualified veto by the three-member Presidency Council essentially required near unanimity among the nine parties of the governing coalition. Given the policy positions of these parties, unanimity was not possible. Our analysis makes use of a fuzzy veto players model. The placement of the government parties along a single dimension based on fuzzy preference measures derived from party text data reveals no common area of agreement

t-Norm Fuzzy Incidence Graphs

It is the case that, in certain applications of fuzzy graphs, a t-norm, instead of a minimum, is more suitable. This requires the development of a new theory of fuzzy graphs involving an arbitrary t-norm in the basic definition of a fuzzy graph. There is very little known about this type of fuzzy graph. The purpose of this paper is to further develop this type of fuzzy graph. We concentrate on the relatively new concept of fuzzy incidence graphs

Similarity of Country Rankings on Sustainability Performance

In this paper‎, ‎we extend the fuzzy similarity measure of‎ ‎two rankings to any finite number of rankings‎. ‎We provide a method to‎ ‎convert a measure for a finite number of rankings to a number that‎ ‎represents the number for two rankings‎. ‎We apply our results to the‎ ‎sustainability ranking of countries by the Environmental Performance Index‎ ‎(EPI)‎. ‎The $2020$ EPI provides a summary of the state of sustainability‎ ‎around the world‎. ‎It uses $32$ performance indicators across $11$‎ ‎categories‎. ‎These indicators provide a way to determine problems‎, ‎set‎ ‎targets‎, ‎track trends‎, ‎understand outcomes‎, ‎and identify best policy‎ ‎practices‎. ‎The EPI ranks $180$ countries on environmental health and‎ ‎ecosystem vitality‎. ‎The EPI provides a method in support of efforts to meet‎ ‎the targets of the UN Sustainable Development Goals‎. ‎The EPI determined‎ ‎that the Global West region ranked the highest‎. ‎The purpose of our project‎ ‎is to find the similarity of the $11$ rankings of the countries for eight‎ ‎different regions‎

Fuzzy Mathematics and Nonstandard Analysis Application to the Theory of Relativity

In this paper, we extend some results of nonstandard analysis to include concepts from fuzzy mathematics. Then we apply our results to issues from special and general relativity and the theory of light-clocks. The extension includes concepts of fuzzy numbers, continuity, and differentiability. Our goal is to provide a new research area in fuzzy mathematics