1 TOPSIS and ELECTRE I Methodologies: Bipolar Fuzzy Formulations . 17 1.1 Introduction . 17 1.2 Bipolar Fuzzy Sets .18 1.3 Multi-criteria Decision Making Methods . 19 1.
4 Bipolar Fuzzy TOPSIS Method . 22 1.5 Bipolar Fuzzy ELECTRE I Method . 28 1.6 Comparative Analysis . 37 1.7 Bipolar Fuzzy Extended TOPSIS Method . 38 1.
8 Conclusion . 42 References . 42 2 TOPSIS Method with Trapezoidal Bipolar Fuzzy Numbers . 45 2.1 Introduction . 45 2.2 Bipolar Fuzzy Numbers . 46 2.
3 Bipolar Fuzzy Linguistic Variables . 48 2.4 Ranking of Bipolar Fuzzy Numbers . 50 2.5 (α, β)-Cut of Bipolar Fuzzy Numbers . 52 2.6 TOPSIS Method Based on Trapezoidal Bipolar Fuzzy Numbers . 58 2.
7 Trapezoidal Bipolar Fuzzy Information System . 65 2.8 Conclusion . 69 References . 69 3 VIKOR Method with Trapezoidal Bipolar Fuzzy Sets . 71 3.1 Introduction . 71 3.
2 Trapezoidal Bipolar Fuzzy VIKOR Method . 74 3.3 Comparative Analysis with Trapezoidal Bipolar Fuzzy TOPSIS . 85 3.4 Comparison of Trapezoidal Bipolar Fuzzy VIKOR with Fuzzy VIKOR . 88 3.5 Conclusion . 88 References .
89 4 Extended VIKOR Method Based on Complex Bipolar Fuzzy Sets . 91 4.1 Introduction . 91 4.2 Complex Bipolar Fuzzy Sets . 94 4.3 Structure of Complex Bipolar Fuzzy VIKOR Method . 96 4.
4 Application . 102 4.5 Comparative Analysis . 113 4.6 Merits of the Presented Method . 117 4.7 Conclusion . 118 References .
118 5 Beyond ELECTRE I: A Bipolar Fuzzy ELECTRE II Method . 121 5.1 Introduction . 121 5.2 Bipolar Fuzzy ELECTRE II Method . 122 5.3 Comparative Study and Discussion . 136 5.
3.1 Bipolar Fuzzy TOPSIS Method . 136 5.3.2 Bipolar Fuzzy ELECTRE I Method . 137 5.3.3 Comparison of bipolar fuzzy ELECTRE II Method with fuzzy ELECTRE II Method139 5.
4 Insights and Limitations of the Method Proposed in this Chapter . 140 References . 140 6 Extended PROMETHEE Method with Bipolar Fuzzy Sets . 143 6.1 Introduction . 143 6.2 Bipolar Fuzzy PROMETHEE Method . 145 6.
2.1 Preference Function . 145 6.2.2 The Bipolar Fuzzy PROMETHEE Method . 146 6.3 Comparative Study . 157 6.
4 Insights of the method . 160 References . 161 7 Enhanced Decision-Making Method with Two-Tuple Linguistic Bipolar Fuzzy Sets 165 7.1 Introduction . 165 7.2 The 2-Tuple Linguistic Bipolar Fuzzy Sets . 168 7.3 The 2-Tuple Linguistic Bipolar Fuzzy Heronian Mean Aggregation Operators .
171 7.4 An approach to MAGDM Problem with 2-Tuple Linguistic Bipolar Fuzzy Information . 178 7.5 Numerical Example . 178 7.6 Comparative Analysis . 189 7.7 Advantages of the proposed strategies .
191 7.8 Conclusions . 192 References . 192.