Gromov–Hausdorff convergence of non-Archimedean fuzzy metric spaces

We introduce the notion of the Gromov–Hausdorff fuzzy distance between two non-Archimedean fuzzy metric spaces (in the sense of Kramosil and Michalek). Basic properties involving convergence and the fuzzy version of the completeness theorem are presented. We show that the topological properties induced by the classic Gromov–Hausdorff distance on metric spaces can be deduced from our approach

On the convergence of two-dimensional fuzzy Volterra-Fredholm integral equations by using Picard method

In this paper we prove convergence of the method of successive approximations used to approximate the solution of nonlinear two-dimensional Volterra-Fredholm integral equations and define the notion of numerical stability of the algorithm with respect to the choice of the first iteration. Also we present an iterative procedure to solve such equations. Finally, the method is illustrated by solving some examples

Hyperspace of a fuzzy quasi-uniform space

[EN] The aim of this paper is to present a fuzzy counterpart method of constructing the Hausdorff quasi-uniformity of a crisp quasi-uniformity. This process, based on previous works due to Morsi [25] and Georgescu [9], allows to extend probabilistic and Hutton [0, 1]-quasi-uniformities on a set X to its power set. In this way, we obtain an endofunctor for each one of the categories of those objects. We will demonstrate the commutativity of these endofunctors with Lowen and Katsaras' functors. Furthermore, we will prove the compatibility of our construction with the Hausdorff fuzzy quasi-pseudometric introduced in [33].The second author is supported by the grant MTM2015-64373-P (MINECO/FEDER, UE). The authors are grateful to the reviewers for useful comments which have improved the first version of the paperPedraza Aguilera, T.; Rodríguez López, J. (2020). Hyperspace of a fuzzy quasi-uniform space. Iranian Journal of Fuzzy Systems. 17(2):97-114. https://doi.org/10.22111/IJFS.2020.5222S9711417

A walk in the noncommutative garden

This text is written for the volume of the school/conference "Noncommutative Geometry 2005" held at IPM Tehran. It gives a survey of methods and results in noncommutative geometry, based on a discussion of significant examples of noncommutative spaces in geometry, number theory, and physics. The paper also contains an outline (the ``Tehran program'') of ongoing joint work with Consani on the noncommutative geometry of the adeles class space and its relation to number theoretic questions.Comment: 106 pages, LaTeX, 23 figure