Fuzziness plays an essential role in the real world. Fuzzy set theory has been developed very fast since it was introduced by Zadeh (1965) [1]. A fuzzy set was characterized with its membership function by Zadeh. The term fuzzy variable was fist introduced by Kaufmann (1975) [2], and then appeared in Zadeh (1978) [3] and Nahmias (1978) [4] as a fuzzy set of real numbers. In order to establish t...

Here we consider the Kohonen algorithm with a constant learning rate as a Markov process evolving in a topological space.It is shown that the process is an irreducible and aperiodic T-chain, regardless of the dimension of both data space and network and the special shape of the neighborhood function.Moreover the validity of Deoblin's condition is proved. These imply the convergence in distribut...

This paper presents a continuous version of the model of distribution dynamics to analyse the transition dynamics and implied long-run behaviour of the EU-27 NUTS-2 regions over the period 1995–2003. It departs from previous research in two respects: first, by introducing kernel estimation and three-dimensional stacked conditional density plots as well as highest density regions plots for the v...

the presence of noise in geophysical measurements has undesirable effects on the seismic data. one of the important problems in seismic data processing is attenuation of the noise to the desired form and keeping the original signal. contamination of seismic data with noise prevents obtaining a proper image of geological structures and seismic data interpretation. in some of the receivers the no...

Convergence hypothesis is one of the results of neoclassical growth model, which has been examined recently. This hypothesis has two forms of absolute and conditional Beta-convergence and implies that regions with lower per capita output have higher per capita growth rates. Since there is no data for regional GDP in Iran, there has been n study to test convergence hypothesis in Iran. Our main c...

In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $top$-filters, namely $top$-convergence spaces, and show the category of $top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of$top$-convergence spaces and that of strong $L$-topological spaces is establish...

In this work we derive a variant of the classic Glivenko-Cantelli Theorem, which asserts uniform convergence of the empirical Cumulative Distribution Function (CDF) to the CDF of the underlying distribution. Our variant allows for tighter convergence bounds for extreme values of the CDF. We apply our bound in the context of revenue learning, which is a well-studied problem in economics and algo...

Suppose (f,X , ν) is a dynamical system and φ : X → R is an observation with a unique maximum at a (generic) point in X . We consider the time series of successive maxima Mn(x) := max{φ(x), . . . ,φ ◦ fn−1(x)}. Recent works have focused on the distributional convergence of such maxima (under suitable normalization) to an extreme value distribution. In this article, for certain dynamical systems...