This book presents a proposal for a new soft computing innovative method called by "CFE" forevaluation of the football matches of FIFA(IFAB) and UEFA to compute the true 'Winner'. It is a research work in the area of 'Football Science', being proposed to FIFA (IFAB) and UEFA, Zurich, Switzerland for consideration to replace the existing obsolete and weak rules of football matches of 90 minutes to declare the final 'Winner'. In CFE, the final decision about any football match of 90 minutes is obtained "by computation", by execution of a software called by 'CFE-software' with the real time input values directly from the field on a number of highly significant parameters, some of them being continuous variables. The result of m-n goals at the end of 90 minutes play in a football match is just one of the many parameters for the computation of the 'Winner' in our proposed CFE method. The evaluation is mainly based upon the application of Fuzzy Logic, 'Fuzzy Pocket Machine', fast Computer Server, good Communication system from playing-field to the server (as used in Cricket matches) and the CFE-software at the server. The Referees need not be experts in fuzzy set theory; they can be easily trained within just 30 minutes of demonstration on : how to use the 'fuzzy pocket machine' for giving real time inputs to the database at the server.

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 (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.