Ranking fuzzy numbers, a significant component in decision making process, supports a decision maker in selecting the optimal solution. Althoung there are many existing ranking methods for fuzzy numbers, most of them suffer from some shortcomings. To overcome these shortcomings, this study proposes a new ranking approach for both normal and generalized fuzzy numbers that ensures full consideration of all information of fuzzy numbers. The proposed approach integrates the concept of centroid point, the left and the right (LR) areas between fuzzy numbers, height of a fuzzy number and the degree of decision maker’s optimism. Several numerical examples are presented to illustrate the efficiency and superiority of the proposed.
To reduce uncertainty in decision making and avoid loss of information, this study also proposed a new fuzzy multi-criteria decision making (MCDM) approach based on the proposed ranking method for generalized fuzzy numbers. The applicability of the proposed fuzzy MCMD model is illustrated through a case study.

ABSTRACT I
ACKNOWLEDGEMENT III
TABLE OF CONTENTS IV
LIST OF TABLES VI
LIST OF FIGURES VII
CHAPTER 1. INTRODUCTION 1
1.1. Research background and motivation 1
1.2. Research objectives and contributions 5
1.3. Research framework 5
CHAPTER 2. FUNDAMENTALS 7
2.1. Classical sets (crisp sets) 7
2.2. Fuzzy sets 7
2.2.1. Terminology and Notation 7
2.2.2. Basic definitions 8
2.2.2.1 Linguistic variables: 9
2.2.2.2 Fuzzy arithmetic 9
2.2.2.3 Basic definitions of triangular and trapezoidal fuzzy numbers 10
2.2.2.4 Arithmetic operations for generalized fuzzy numbers 13
2.2.2.5 Basic properties of fuzzy quantities 14
CHAPTER 3. REVIEW OF EXISTING APPROACHES FOR RANKING FUZZY NUMBERS 15
3.1. Centroid approaches 15
3.2. Deviation degree approaches 17
3.2.1. Wang et al.’s approach 17
3.2.2. Nejad and Mashinchi’s approach 19
3.2.3. Asady’s approach 20
3.3. Magnitude approaches for ranking fuzzy numbers 21
3.4. Chen and Chen’s approaches 24
3.5. Kumar et al.’s approaches 26
CHAPTER 4. THE PROPOSED APPROACHES FOR RANKING FUZZY NUMBERS 30
4.1. The proposed epsilon-deviation degree approach 30
4.1.1. Shortcomings of deviation degree approaches 30
4.1.2. The proposed epsilon-deviation degree approach 34
4.1.3. Comparison the proposed epsilon degree approach with other existing approaches 38
4.2. The proposed approach for ranking generalized fuzzy numbers based on centroid and rank index 49
4.2.1. Shortcomings of Kumar et al.’s approach 49
4.2.2. The proposed approach 53
4.2.3. Comparison of the proposed approach with existing approaches 55
CHAPTER 5. THE PROPOSED FUZZY MCDM APPROACH 61
5.1. The proposed fuzzy MCDM approach 61
5.2. Ilustrated example 64
CHAPTER 6. CONCLUSIONS AND FUTURE RESEARCH DIRECTIONS 68
6.1. Conclusions 68
6.2. Recommendations for further research 69
REFERENCE 71

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