The work in this book is based on philosophical as well as logical views on the subject of decoding  the ‘progress’ of  decision making process in the cognition system of a decision maker (be it a human or an animal or a bird or any living thing which has a brain) while evaluating the membership value µ(x)  in a fuzzy set  or in an intuitionistic fuzzy set or in any such soft computing set model or in a crisp set.  A new theory is introduced called by “Theory of CIFS”.   The following two hypothesis are hidden facts in fuzzy computing or in any soft computing process :- Fact-1: A decision maker (intelligent agent)  can never use or apply  ‘fuzzy theory’ or any soft-computing set theory without intuitionistic fuzzy system. Fact-2 : The Fact-1 does not necessarily require that a fuzzy decision maker (or a crisp ordinary decision maker or a decision maker with any other soft theory models or a decision maker like animal/bird which has brain, etc.)  must be aware or knowledgeable about IFS Theory! The “Theory of CIFS” is developed with a careful analysis unearthing the correctness of these two facts. Two examples of ‘decision making problems’ with complete solutions are presented out of which one example will show the dominance of the application potential of intuitionistic fuzzy set theory over fuzzy set theory, and the other will show the converse  i.e. the dominance of the application potential of fuzzy set theory over intuitionistic fuzzy set theory in some cases. The “Theory of CIFS” may be viewed to belong to the subjects : Theory of Intuitionistic Fuzzy Sets, Soft Computing, Artificial Intelligence, etc.