2001, Vol. VIII, Núm. 1
http://hdl.handle.net/2099/2072
2015-10-14T04:39:50ZGeneration of fuzzy mathematical morphologies
http://hdl.handle.net/2099/3595
Generation of fuzzy mathematical morphologies
Burillo López, Pedro; Frago Paños, Noé; Fuentes-González, Ramón
Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In
order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a
general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones
existing in related literature
In the definition of fuzzy erosion and dilation we use several fuzzy implications (Annexe A, Table of fuzzy
implications), the paper includes a study on their practical effects on digital image processing. We also present some
graphic examples of erosion and dilation with three different structuring elements $B(i, j)=1$, $B(i, j)=0.7$, $B(i, j)=0.4$, $i, j \in \{ 1,2, 3\}$ and various fuzzy implications.
2001-01-01T00:00:00ZOn four intuitionistic fuzzy topological operators
http://hdl.handle.net/2099/3594
On four intuitionistic fuzzy topological operators
Atanassov, Krassimir T.
Four new operators, which are analogous of the topological operators "interior" and "closure", are defined. Some of their basic properties are studied. Their geometrical interpretations are given.
2001-01-01T00:00:00ZA theorem for basis operators over intuitionistic fuzzy sets
http://hdl.handle.net/2099/3593
A theorem for basis operators over intuitionistic fuzzy sets
Atanassov, Krassimir T.
The concept of s-basis operators over intuitionistic fuzzy sets is introduced and all 2-, 2-, 4-, basis operators are listed.
2001-01-01T00:00:00ZTopological automorphism groups of chains
http://hdl.handle.net/2099/3592
Topological automorphism groups of chains
Ovchinnikov, Sergei V.
It is shown that any set--open topology on the automorphism group $A(X)$ of a chain $X$ coincides with the pointwise topology and that $A(X)$ is a topological group with respect to this topology. Topological properties of connectedness and compactness in $A(X)$ are investigated. In particular, it is shown that the automorphism group of a doubly homogeneous chain is generated by any neighborhood of the identity element.
2001-01-01T00:00:00ZApplication of Cauchy's equation in combinatorics and genetics
http://hdl.handle.net/2099/3591
Application of Cauchy's equation in combinatorics and genetics
Kannappan, Palaniappan
We are familiar with the
combinatorial formula
$\left(\begin{array}{cc}
n\\
r
\end{array}\right) = \frac{n(n-1) \cdots (n - r +
1)}{r !} = $ number
of possible ways of choosing $r$ objects out of $n$ objects\,.
In section 1 of this paper we obtain $\left(
\begin{array}{cc} n\\
2\end{array}\right)$ and $\left( \begin{array}{cc}
n\\
3
\end{array}\right)$ by using a functional equation, {\it
the additive Cauchy equation}.
In genetics it is important to know the combinatorial
function $g_{r}(n)=$ the number of possible ways of
picking $r$ objects at a time from $n$ objects {\it
allowing repetitions}, since this function describes the
number of possibilities from a gene pool. Again we determine $g_2(n)$ and $g_3(n)$ with the help of the additive Cauchy equation in section 2.
Functional equations are used increasingly in diverse
fields. The method of finding $\left( \begin{array}{cc}
n\\
2
\end{array}\right), \left( \begin{array}{cc}
n\\
3
\end{array}\right), g_2 (n)$ and $g_3(n)$ (see Snow [6])
is similar to that of finding the well known sum of
powers of integers $S_K(n) = 1^K + 2^K + \cdots + n^K$
(Acz\'{e}l [2], Snow [5]).\\
2001-01-01T00:00:00ZOn the generalizations of Siegel's fixed point theorem
http://hdl.handle.net/2099/3590
On the generalizations of Siegel's fixed point theorem
Jung, J.S.; Chang, S.S.; Lee, B.S.; Cho, Y.J; Kang, S.M.
In this paper, we establish a new version of Siegel's fixed point
theorem in generating spaces of quasi-metric family. As consequences, we obtain
general versions of the Downing-Kirk's fixed point and Caristi's fixed point
theorem in the same spaces. Some applications of these results to fuzzy metric
spaces and probabilistic metric spaces are presented.
2001-01-01T00:00:00Z