The theory and methods of the multiple attribute decision making have been extensively applied to the fields of engineering project, economy, management and military, such as investment decision making, venture capital project evaluation, facility location, maintenance services, bidding, development ranking of industrial sectors, comprehensive evaluation of economic performance etc. With the increasing complexity and uncertainty of objective things, the fuzziness of human thought, and poor information more and more attention has been paid to the investigation on multiple attribute decision making under uncertain environments such as the fuzziness and greyness. This book offers a systematic introduction to the methods for the grey hybrid multi-attribute decision making and their applications to various practical problems. In particular, we extend our work and offer a more comprehensive overview of our papers.