The QL&SC 2012 is a major symposium for scientists, and practitioners all around the world to present their latest researches, results, ideas, developments and applications in such areas as quantitative logic, many-valued logic, fuzzy logic, quantification of software, artificial intelligence, fuzzy sets and systems and soft computing.This invaluable book provides a broad introduction to the fuzzy reasoning and soft computing. It is certain one should not go too far in approximation and optimization, and a certain degree must be kept in mind. This is the essential idea of quantitative logic and soft computing.The explanations in the book are complete to provide the necessary background material needed to go further into the subject and explore the research literature. It is suitable reading for graduate students. It provides a platform for mutual exchanges from top experts and scholars around the world in this field.