makeidx \printindex problem, is there one way to redefine index name as chapter format

Question

I am using makeidx package, when use \printindex command, it will be start in new page,

Is there one way to let "Index" name as chapter style, just like "Chapter 1 Index".

I want to change the index definition, but I can't find it.

Is there anybody could help me.

\documentclass[]{book}

\usepackage{makeidx} 
\makeindex


\begin{document}

test test test test\index{AAA} test test test test\index{BBB} test test test test test\index{CCC} test test test test test test test test test test test test test test test test test test test\index{DDD} test test test test test test 


\printindex

\end{document}

Answer 1

Solution 1:

\documentclass[]{book}

\usepackage{makeidx} 
\makeindex
\renewcommand{\indexname}{\chaptername\ \thechapter\ Index}


\begin{document}

\chapter{First}
test test test test\index{AAA} test test test test\index{BBB} test test test test test\index{CCC} test test test test test test test test test test test test test test test test test test test\index{DDD} test test test test test test 

\stepcounter{chapter}
\printindex

\end{document}

Produces:

Solution 2

(with redefinition of index environment):

\documentclass[openany]{book}
\usepackage{makeidx}

\makeatletter
\renewenvironment{theindex}
               {\if@twocolumn
                  \@restonecolfalse
                \else
                  \@restonecoltrue
                \fi
                %\twocolumn[\@makeschapterhead{\indexname}]%NO PAGEBREAK BEFORE INDEX
                \@mkboth{\MakeUppercase\indexname}%
                        {\MakeUppercase\indexname}%
                \thispagestyle{plain}\parindent\z@
                \parskip\z@ \@plus .3\p@\relax
                \columnseprule \z@
                \columnsep 35\p@
                \let\item\@idxitem}
                %{\if@restonecol\onecolumn\else\clearpage\fi} %NO CLEARPAGE AFTER INDEX
\makeatother

\makeindex

\begin{document}

\chapter{First Chapter}
A\index{A}B\index{B}

\chapter{Index}
\printindex

\chapter{Other chapter}

\end{document}

Produces: