Any way to reference a particular component of a label?

The cleveref package provides some machinery to "strip" the prefix component from an object's number when creating cross-references to ranges of objects, such as figure environments.

For more information on this method, see page 20 of the user guide of the cleveref package as well as postings such as Referencing a range of equations with a particular format (A.3-7) instead of (A.3)-(A.7) and Crossreference in Ref Range (1a-1e) to (1a-e).

\documentclass[runningheads]{llncs}
\usepackage{amsmath}   % for '\numberwithin' macro
\numberwithin{figure}{section}

\usepackage[noabbrev]{cleveref}  % see https://ctan.org/pkg/cleveref
\crefrangelabelformat{figure}{#3#1#4--#5\crefstripprefix{#1}{#2}#6}

\begin{document}
%% The following is _minimalist_ code
\setcounter{section}{1}
\refstepcounter{figure}\label{fig:aa}
\refstepcounter{figure}\label{fig:bb}
\refstepcounter{figure}\label{fig:cc}

A cross-reference to \cref{fig:aa,fig:cc,fig:bb}. % arguments of '\cref' needen't be sorted by the user
\end {document}

---

Addendum: The solution method proposed here lets writers use \cref to create multiple cross-referencing call-outs to ranges of numbers, with the number prefix being stripped off for each range of numbers. For instance,

\documentclass[runningheads]{llncs}
\counterwithin{figure}{section}

\usepackage[noabbrev]{cleveref}  % see https://ctan.org/pkg/cleveref
\crefrangelabelformat{figure}{#3#1#4--#5\crefstripprefix{#1}{#2}#6}

\begin{document}
%% The following is _minimalist_ code; it's not how one would normally
%% go about creating 'figure' environments, captions, and labels.
\setcounter{section}{1}
\refstepcounter{figure}\label{fig:aa} % 1.1
\refstepcounter{figure}\label{fig:bb} % 1.2
\refstepcounter{figure}\label{fig:cc} % 1.3
\stepcounter{section}
\refstepcounter{figure}\label{fig:dd} % 2.1
\refstepcounter{figure}\label{fig:ee} % 2.2
\refstepcounter{figure}\label{fig:ff} % 2.3
\refstepcounter{figure}\label{fig:gg} % 2.4

%% Now the call to \cref. Note that the arguments of \cref
%% need not be sorted in any order.
A cross-reference to \cref{fig:aa,fig:cc,fig:gg,fig:ee,fig:ff,fig:bb}. 
\end {document}

If you're not using any fancy cross-referencing packages, you can just set the reference to whatever you like before setting a \label by changing \@currentlabel:

\documentclass[runningheads]{llncs}

\usepackage{mathtools}

\numberwithin{figure}{section}

\begin{document}

\section{A section}

See Figures \ref{fig:first}--\ref{fig:final}, 
or Figures~\ref{fig:first}--\ref{fig:final-final}.

\begin{figure}
  \caption{First figure}\label{fig:first}% 1.1
  \caption{Second figure}\label{fig:second}% 1.2
  \caption{Third figure}\label{fig:third}% 1.3
  \caption{Final figure}\label{fig:final}% 1.4
  \makeatletter
  \renewcommand{\@currentlabel}{\arabic{figure}}\label{fig:final-final}% 4
  \makeatother
\end{figure}

\end{document}

You can load the package refcount and define a macro \RefOnlyStuffBehindLastDot which uses refcount's \getrefbykeydefault for extracting the number from the reference before applying a tail-recursive macro which from the extracted number removes dot-delimited arguments until no dots are left:

\documentclass[runningheads]{llncs}

\usepackage{refcount}
\makeatletter
\@ifdefinable\gobbletodot{\long\def\gobbletodot#1.{}}%
\newcommand\KeepOnlyStuffBehindLastDot[1]{%
  \ifcat$\detokenize\expandafter{\gobbletodot#1.}$%
  \expandafter\@firstoftwo\else\expandafter\@secondoftwo\fi
  {#1}{\expandafter\KeepOnlyStuffBehindLastDot\expandafter{\gobbletodot#1}}%
}%
\@ifdefinable\RefOnlyStuffBehindLastDot{%
  \DeclareRobustCommand\RefOnlyStuffBehindLastDot[1]{%
    \IfRefUndefinedBabel{#1}{\refused{#1}\nfss@text{\reset@font\bfseries??}}%
                        {%
                          \@ifundefined{hyperref}{\@firstofone}{\hyperref[{#1}]}%
                          {%
                            \expandafter\expandafter\expandafter\KeepOnlyStuffBehindLastDot
                            \expandafter\expandafter\expandafter{\getrefbykeydefault{#1}{}{??}}%
                          }%
                        }%
  }%
}%
\makeatother

% \usepackage{hyperref}

\let\proof\relax
\let\endproof\relax

\usepackage{amsthm}
\usepackage{amssymb}
\setcounter{tocdepth}{3}
\usepackage{graphicx}
\usepackage{mathtools}
\usepackage{listings}
\usepackage{verbatim}
\usepackage{epsfig}  
\usepackage[linesnumbered,ruled,vlined]{algorithm2e}
\usepackage{todonotes}
\usepackage[normalem]{ulem}
\usepackage{proof}
\usepackage{ragged2e}
\usepackage{enumitem}
\usepackage{syntax}
\usepackage{mathpartir}

\numberwithin{figure}{section}

\begin{document}

\title{Example}
\titlerunning{Example}

\author{Me}

\maketitle

\section{First Section}

\begin{figure}[htbp]
\caption{First Figure}
\label{fig:1.1}
This is a figure.
\end{figure}

\begin{figure}[htbp]
\caption{Second Figure}
\label{fig:1.2}
This is another figure.
\end{figure}

\begin{figure}[htbp]
\caption{Third Figure}
\label{fig:1.3}
This is yet another figure.
\end{figure}

\section{Second Section}

\begin{figure}[htbp]
\caption{Fourth Figure}
\label{fig:2.1}
This is a figure in the second section.
\end{figure}

\begin{figure}[htbp]
\caption{Fifth Figure}
\label{fig:2.2}
This is another figure in the second section.
\end{figure}

\section{Conclusion}
As you can see in figures \ref{fig:1.1}-\ref{fig:1.3}, the numbering is not what I'd like. I want it to read "figures 1.1-3".

As you can see in figures \ref{fig:1.1}-\RefOnlyStuffBehindLastDot{fig:1.3}, the numbering what I like. I want it to read "figures 1.1-3".

\end{document}