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. پرونده مقاله

It has been shown in [3] that in the two-dimensional case, the lattices of truth values considered are pairwise isomorphic, and so are the corresponding families of fuzzy sets. Therefore, each result for one of these types of fuzzy sets can be directly rewritten for each (isomorphic) type of fuzzy sets. In this paper, we show that there is a strong connection between weighted graphs and fuzzy graphs. We accomplish this by using lattice isomorphisms. Consequently, under certain conditions, results for one area can be carried over immediately to the other. Many situations in fuzzy graph theory do not depend on the weights of the vertices. The situation of providing weights for the vertices of a weighted graph is also considered. We also consider lattice homomorphisms with an illustration involving nonstandard analysis. In particular, we consider a nonstandard weighted graph, i.e., a graph where the weights of the edges are from a nonstandard interval. پرونده مقاله

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 [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 پرونده مقاله

We use a new method to determine a fuzzy similarity measure using fuzzy implication operators‎. ‎We use this method to determine the fuzzy similarity between the two rankings of countries involving health security and health care‎. ‎We then find a fuzzy similarity of countries involving the two rankings of countries with respect to national disaster‎ ‎and political disaster‎. پرونده مقاله

In this paper, we discuss how theoretical results from one family of fuzzy sets can be carried over immediately to another family of fuzzy sets by the use of lattice isomorphisms. We also show that these families can occur naturally and that applications may not necessarily be carried over using these isomorphisms. We illustrate this using techniques from the study of human trafficking and its analysis using mathematics of uncertainty. We also consider the new definition of fuzzy set provided by Trillas and de Soto. پرونده مقاله