I am searching fo an appropriate symbol in latex for the concatenation between two sets
Thanks,
I want a symbol like this in the following
image
A great resource for this kind of question is the opaquely named Detexify, at http://detexify.kirelabs.org/classify.html. You sketch a shape with the mouse and it lists the TeX symbols that look like it, along with package and mode information. It did a great job with my very clumsy rendering of your symbol, finding as top matches the same symbols proposed by egreg and LaRiFaRi:

Your symbol seems \smallfrown from amssymb, but raised up.
\documentclass{article}
\usepackage{amsmath,amssymb}
\newcommand{\tieconcat}{%
\mathbin{\mathpalette\dotieconcat\relax}%
}
\newcommand{\dotieconcat}[2]{% auxiliary macro, don't use it directly
\text{\raisebox{.8ex}{$\smallfrown$}}%
}
\begin{document}
$A\tieconcat B$
$A\sqcup B$
\end{document}
The symbol I prefer, though, is \sqcup that I showed at the bottom.

If you are able to use Lua- or XeLaTeX, you can just use the Unicode of this symbol which is U+2040. There will be quite a lot of fonts on your system that support this symbol. You could choose one, load the package fontspec and do: \newcommand*{\concat}{\fontspec{your-font-name}\mathbin{\text{\symbol{"2040}}}}.
However, it would be easier to use the command \tieconcat which is part of the unicode-math package. The fonts XITS and Asana do provide that symbol. This could look like the following:
% arara: lualatex
\documentclass{article}
\usepackage{unicode-math}
\begin{document}
\setmathfont{XITS Math}
\[
A\tieconcat B
\]
\setmathfont{Asana Math}
\[
A\tieconcat B
\]
\end{document}

If you want to use PDFLaTeX, you will have to use \frown from mathtools or MnSymbol or for a narrower version \smallfrown from amssymb.
You can reproduce your symbol by raising them a bit up. Just adapt the 0.9ex until you find it pleasing.
% arara: pdflatex
\documentclass{article}
\usepackage{amssymb}
\usepackage{mathtools}
\newcommand*{\upFrown}{\mathbin{\raisebox{0.9ex}{$\frown$}}}
\newcommand*{\upSmallFrown}{\mathbin{\raisebox{0.9ex}{$\smallfrown$}}}
\begin{document}
$A\upFrown B \upSmallFrown C$
\end{document}

$\cup$for a set union. – quinmars Sep 27 '14 at 08:50