Here is one approach using enumitem hiding the list in an mbox:

\documentclass{article}
\usepackage{enumitem}
\newlist{eqlist}{enumerate*}{1}
\setlist[eqlist]{itemjoin=\quad,mode=unboxed,label=(\roman*),ref=\theequation(\roman*)}
\begin{document}
\setcounter{equation}{17}
\begin{equation}
\label{eq:three}
\mbox{%
\begin{eqlist}
\item\label{eqi:th-one} \( x>y\),
\item\label{eqi:th-two} \( y>z\),
\item\label{eqi:th-three} \( \displaystyle z>\int_{0}^{1} e^{x^{2}}dx \).
\end{eqlist}}
\end{equation}
Referencing (\ref{eqi:th-two}).
\end{document}
However, this will not work with amsmath (because of the multiple label commands) and does not allow multiple lines. A varation solving both problems is the following, based on minipage:

\documentclass{article}
\usepackage{enumitem,amsmath}
\newlist{eqlist}{enumerate*}{1}
\makeatletter
\setlist[eqlist]{itemjoin=\quad,mode=unboxed,label=(\roman*),
ref=\theequation(\roman*),before={\let\label\ltx@label}}
\makeatother
\begin{document}
\setcounter{equation}{17}
\begin{equation}
\label{eq:three}
\begin{minipage}{.8\linewidth}\centering
\begin{eqlist}
\item\label{eqi:th-one} \( x>y\),
\item\label{eqi:th-two} \( y>z\),
\item\label{eqi:th-three} \( \displaystyle z>\int_{0}^{1}
e^{x^{2}}dx \),\endgraf
\item\label{eqi:th-four} \( \displaystyle a = \int_{U} \frac{\cos
x}{\sin y}\,dx\,dy\).
\end{eqlist}
\end{minipage}
\end{equation}
Referencing \eqref{eqi:th-two} and \eqref{eqi:th-four}.
\end{document}