FUZZY SETS AND SOME OF ITS APPLICATIONS

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ABSTRACT

In 1999, Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Alkhazaleh and Salleh (2011) define the concept of soft expert sets where the user can know the opinion of all experts in one model and give an application of this concept in decision making problem. So in this paper, we generalize the concept of a soft expert set to fuzzy soft expert set, which will be more effective and useful. We also define its basic operations, namely complement, union, intersection, AND and OR. We give an application of this concept in decision making problem. Finally, we study a mapping on fuzzy soft expert classes and its properties.

DECLARATION.. ii

CERTIFICATION.. iii

DEDICATION.. iv

ACKNOWLEDGEMENT. v

ABSTRACT. vi

CHAPTER ONE. 1

INTRODUCTION.. 1

1.0 BACKGROUND OF STUDY.. 1

1.1 Statement of problem.. 2

1.2 Aim and Objectives 4

1.3 Definition of key terms 4

CHAPTER TWO.. 7

LITERATURE REVIEW.. 7

2.1 A REVIEW ON THE STUDY OF FUZZY SOFT SETS. 7

2.2   A REVIEW OF COMPARISON ON THE STUDY OF SOFT SET AND FUZZY SET. 8

CHAPTER THREE. 11

FUNDAMENTALS OF FUZZY SOFT SET THEORY.. 11

3.1 INTRODUCTION.. 11

3.2 Fuzzy Soft Sets 12

3.4 Algebraic Structures of Fuzzy Soft Sets 18

CHAPTER FOUR. 20

SOME APPLICATIONS OF FUZZY SOFT SET THEORY.. 20

4.1 INTRODUCTION.. 20

4.2 Fuzzy Soft Set in Industrial Engineering. 20

4.2.1 Statistical Decision-Making. 21

4.2.2 Manufacturing. 23

4.3  Fuzzy application in Game theory. 25

CHAPTER FIVE. 27

SUMMARY, CONCLUSION AND RECOMMENDATION(S) 27

5.0 Summary. 27

5.1 Conclusion. 27

5.2 Recommendations 28

REFERENCES. 29

CHAPTER ONE

INTRODUCTION

1.1 Background of Study

Molodtsov Proposed a completely new approach for modeling vagueness and uncertainty soft set theory. Most of its applications have already been demonstrated in  Fuzzy soft set theory has been proposed and has potential applications. In recent years, soft set and fuzzy soft set theories have been proved to be useful in many different fields, such as decision making, data analysis, forecasting, simulation, evaluation of sound quality and rule mining. The study of hybrid models combining soft sets or fuzzy soft sets with other mathematical structures and new operations are emerging as an active research topic of soft set theory. Maji et al. considered the reduct soft set with the help of rough set approach and discussed soft set theory.

Roy et al. discussed score value as the evaluation basis to make decisions in fuzzy soft sets. Zhi Kong et al. analyzed two decision evaluation bases, choice value and score value, and used a counter example to discuss the two methods , Naim Çagman et al. presented soft matrix theory and uni-int decision making. Yuncheng Jiang et al. introduced two methods, semantic decision making using ontology and intuitionistic fuzzy soft set decision making, and extended soft sets with description logics, discussing interval-valued intuitionistic fuzzy soft set properties. Feng Feng et al. presented an adjustable approach by means of level soft sets and interval-value fuzzy soft sets, and soft semirings and soft rough sets. Xibei Yan et al. introduced the concept of interval-valued fuzzy soft sets and discussed its operations. Ke Gong et al. discussed the bijective soft set and its operations. Hacı Aktaş et al. discussed soft sets and soft groups. Hailong Yang presented kernels and closures of soft set relations and soft set relation mappings. Pinaki Majumdar et al. introduced generalized fuzzy soft sets. Young Bae Jun et al. and Jianming Zhan et al. discussed algebras soft sets. Wei Xu et al. presented vague soft sets and their properties. Muhammad Irfan Ali et al. discussed some new operations in soft set theory and approximation space associated with each parameter in a soft set. Babitha et al. presented soft set relations and functions. Ummahan Acar et al. presented soft sets and soft rings. Zhi Xiao et al. introduced exclusive soft sets. Chen et al. presented a definition of parameterization reduction in soft set theory, and compared this definition to the related concept of attributes reduction in rough set theory.

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