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This is the first book to provide a comprehensive and systematic introduction to the ranking methods for interval-valued intuitionistic fuzzy sets, multi-criteria decision-making methods with interval-valued intuitionistic fuzzy sets, and group decision-making methods with interval-valued intuitionistic fuzzy preference relations. Including numerous application examples and illustrations with tables and figures and presenting the authors' latest research developments, it is a valuable resource for researchers and professionals in the fields of fuzzy mathematics, operations research, information science, management science and decision analysis.