The notion of intuitionistic fuzzy set has received a lot of attention in the recent years, especially as a tool to deal with uncertainty. This book aims to outline the main results in the area in concise manner, to provide a useful summary of similar concepts and how they relate to intuitionistic fuzzy sets, and to show that some of the claimed “extensions” proposed by different authors are in fact incorrect, redundant, etc. It also highlights new venues for research and defines currently open problems which could serve all interested researchers as a roadmap in their investigations.