A Study of the Fundamentals of Fuzzy Set

Abstract

The fundamental idea of the project is to provide basic and concrete concepts of the fuzzy set theory, and thus focused on easy illustrations of the basic concepts. There are numerous examples and figures to help readers to understand. It tries to explain the emergence of fuzzy sets from historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's works have cristalized and popularized a concern that has appeared in the first half of the century, mainly in philosophical circles. Another purpose of the project is to scan the basic definitions in the field. This project also contains a discussion on operational semantics of the generally two abstract notion of membership function.

TABLE OF CONTENTS 

TITLE PAGE   ………………………………………………………………….         

i CERTIFICATION PAGE ………………………………………………………        

ii DELARATION PAGE ………………………………………………………….       

iii DEDICATION PAGE …………………………………………………………..        

iv ACKNOWLEDGEMENTS ……………………………………………………..        

v ABSTRACT………………………………………………………………………       

vi TABLE OF CONTENTS …………………………………………………………     

CHAPTER ONE           

GENERAL INTRODUCTION……………………….     1

1.1 Introduction ………………………………………………………………………  1

1.2 A review of set theory ……………………………………………………………  4    

1.3 Aims and objectives ……………………………………………………………..   11

1.4 Scope and limitation ……………………………………………………………..   11

1.5 Methodology …………………………………………………………………….    11

CHAPTER TWO 

LITERATURE REVIEW ……………………………………    12

CHAPTER THREE 

FUZZY SET THEORY ……………………………………    16

3.1 Introduction ……………………………………………………………………...    16

3.2 Crisp and non-crisp sets …………………………………………………………     17

3.3 Basic notion of fuzzy set theory …………………………………………………    18

3.4 Some important terms of fuzzy set theory ....................………………………….    20

3.5 Operations on fuzzy sets …………………………………………………………    23

3.6 Cartesian  product  of  two  fuzzy sets  ………………..……………………………      26  

3.7 Properties of fuzzy sets …………………………………………………………….. 27

CHAPTER FOUR 

SUMMARY, CONCLUSION AND REFERRENCES……...…29

4.1 Summary ...……………………………………………...…………………………   29

4.2 Conclusion…………………...…………………………………………………….   30

4.3 References ………………………………………………………………………..     31