Removing the condition of symmetry in the notion of a fuzzy (pseudo)metric, in Kramosil and Michalek’s sense, one has the notion of a fuzzy quasi-(pseudo-)metric. Then for each fuzzy quasi-pseudo-metric on a set X we construct a fuzzy quasipseudo-metric on the collection of all nonempty subsets of X, called the Hausdorff fuzzy quasi-pseudo-metric. We investigate several properties of this struc...

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.

We propose a new approach to assigning distance between fuzzy numbers. A pseudo-metric on the set of fuzzy numbers and a metric on the set of trapezoidal fuzzy numbers are described. The regular reducing functions and the Hausdorff metric are used to define the metric. Using this metric, we can approximate an arbitrary generalized left right fuzzy number with a trapezoidal one. Finally, powers ...

Traditional fuzzy logic systems are unable to handle the uncertainties of real-world applications. By "handle" I mean directly model and minimize the effect of. In this talk I will explain rule-based type-2 fuzzy logic systems and how they can handle a broad range of uncertainties totally within their framework. This is accomplished by adding a new mathematical dimension-a third dimension-to ty...

In this paper, we define asymptotic dimension of fuzzy metric spaces in the sense George and Veeramini. We prove that is an invariant coarse category spaces. also show several consequences setting which resemble setting. finish with calculating a few

J.M. Aarts introduced and studied a new dimension function, Hind, in 1975 and obtained several results on this function. In this paper, a new local inductive dimension function called local huge inductive dimension function denoted by locHind is introduced and studied. Furthermore, an effort is made to introduce and study dimension functions for fuzzy topological spaces. It has been possible to...

This paper evaluates and ranks the temporal dimensions, known as fourth dimension of urban design, of a number of places in a city by TOPSIS method. TOPSIS method is technique for order preference by similarity to ideal solution. TOPSIS is one of the renowned methods for classical multi-criteria decision-making (MCDM) problems that defines the positive ideal solution and negative ideal solution...

The Vapnik-Chervonenkis (VC) dimension measures the complexity of a learning machine, and a low VC dimension leads to good generalization. The recently proposed Minimal Complexity Machine (MCM) learns a hyperplane classifier by minimizing an exact bound on the VC dimension. This paper extends the MCM classifier to the fuzzy domain. The use of a fuzzy membership is known to reduce the effect of ...

In this paper, we propose an approximate "fuzzy Voronoi" diagram (FVD)for fuzzy numbers of dimension two (FNDT) by designing an extension of crisp Voronoi diagram for fuzzy numbers. The fuzzy Voronoi sites are defined as fuzzy numbers of dimension two. In this approach, the fuzzy numbers have a convex continuous differentiable shape. The proposed algorithm has two stages: in the first stage we ...