Is 'Fuzzy Theory' an Appropriate Tool for Large Size Problems?

by Ranjit Biswas

Overview

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.

Product Details

ISBN-13:	9783319267173
Publisher:	Springer International Publishing
Publication date:	12/09/2015
Series:	SpringerBriefs in Applied Sciences and Technology
Edition description:	1st ed. 2016
Pages:	64
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

Two Hidden Facts about Fuzzy Set Theory (and, about any Soft
Computing Set Theory).- Cognitive Intuitionistic Fuzzy System (CIFS).- Is „Fuzzy Theory‟ an Appropriate Tool for Large Size Problems?.- Ordering (or Ranking) of Elements in an IFS on the basis of
Their Amount of Belongingness.- An Application Domain to Understand the Potential of
Intuitionistic Fuzzy Theory over Fuzzy Theory.- An Example of Application Domain to Understand the
Potential of Fuzzy Theory over Intuitionistic Fuzzy Theory in Some Cases.- Conclusion.- Future Research Directions.