Multi-criteria Decision Making Methods with Bipolar Fuzzy Sets (Forum for Interdisciplinary Mathematics)

This monograph discusses the theoretical and practical development of multicriteria decision making (MCDM). The main purpose of MCDM is the construction of systematized strategies for the "optimisation" of feasible options, as well as the justification of why some alternatives can be declared "optimal". However, at time, we must make decisions in an uncertain environment and such inconvenience gives rise to a much more elaborate scenario. This book highlights models where this lack of certainty can be flexibly fitted in and goes on to explore valuable strategies for making decisions under a multiplicity of criteria. Methods discussed include bipolar fuzzy TOPSIS method, bipolar fuzzy ELECTRE-I method, bipolar fuzzy ELECTRE-II method, bipolar fuzzy VIKOR method, bipolar fuzzy PROMETHEE method, and two-tuple linguistic bipolar fuzzy Heronian mean operators. This book is a valuable resource for researchers, computer scientists, and social scientists alike. Foreword Preface Contents About the Authors List of Figures List of Tables 1 TOPSIS and ELECTRE I Methodologies: Bipolar Fuzzy Formulations 1.1 Introduction 1.2 Bipolar Fuzzy Sets 1.3 Multi-criteria Decision Making Methods 1.4 Bipolar Fuzzy TOPSIS Method 1.5 Bipolar Fuzzy ELECTRE I Method 1.6 Comparative Analysis 1.7 Bipolar Fuzzy Extended TOPSIS Method 1.8 Conclusion References 2 TOPSIS Method with Trapezoidal Bipolar Fuzzy Numbers 2.1 Introduction 2.2 Bipolar Fuzzy Numbers 2.3 Bipolar Fuzzy Linguistic Variables 2.4 Ranking of Bipolar Fuzzy Numbers 2.5 (α,β)-Cut of Bipolar Fuzzy Numbers 2.6 TOPSIS Method Based on Trapezoidal Bipolar Fuzzy Numbers 2.7 Trapezoidal Bipolar Fuzzy Information System 2.8 Conclusion References 3 VIKOR Method with Trapezoidal Bipolar Fuzzy Sets 3.1 Introduction 3.2 Trapezoidal Bipolar Fuzzy VIKOR Method 3.3 Comparative Analysis with Trapezoidal Bipolar Fuzzy TOPSIS Method 3.4 Comparative Analysis with Fuzzy VIKOR Method 3.5 Conclusion References 4 Extended VIKOR Method with Complex Bipolar Fuzzy Sets 4.1 Introduction 4.2 Complex Bipolar Fuzzy Sets 4.3 Structure of Complex Bipolar Fuzzy VIKOR Method 4.4 Application 4.5 Comparative Analysis 4.6 Merits of the Presented Method 4.7 Conclusion References 5 Beyond ELECTRE I: A Bipolar Fuzzy ELECTRE II Method 5.1 Introduction 5.2 Bipolar Fuzzy ELECTRE II Method 5.3 Comparative Study and Discussion 5.3.1 Comparison with Bipolar Fuzzy TOPSIS Method 5.3.2 Comparison with Bipolar Fuzzy ELECTRE I Method 5.3.3 Comparison with Fuzzy ELECTRE II Method 5.4 Insights and Limitations of the Proposed Method References 6 Extended PROMETHEE Method with Bipolar Fuzzy Sets 6.1 Introduction 6.2 Bipolar Fuzzy PROMETHEE Method 6.2.1 Preference Function 6.2.2 Structure of Bipolar Fuzzy PROMETHEE Method 6.3 Comparative Study 6.4 Conclusion References 7 Enhanced Decision Making Method with Two-Tuple Linguistic Bipolar Fuzzy Sets 7.1 Introduction 7.2 The 2-Tuple Linguistic Bipolar Fuzzy Sets 7.3 The 2-Tuple Linguistic Bipolar Fuzzy Heronian Mean Aggregation Operators 7.4 An Approach to MAGDM Problem with 2-Tuple ... 7.5 Numerical Example 7.6 Comparative Analysis 7.7 Advantages of the Proposed Strategies 7.8 Conclusions References Index