This book tackles the intricacies of decision-making processes where alternatives stem from distinct, finite sets. Discover the cutting-edge in decision-making with our groundbreaking book on complex two-sided matching methods. Harnessing the power of probabilistic linguistic term sets, it introduces innovative methods that enhance matching efficiency and practicality. It addresses the pressing question of how to navigate and optimize in scenarios with multifaceted matching challenges, offering an exploration into the psychological perceptions of agents through consistency checks and pairwise comparisons. It delves into the unknowns of static matching with multiple attribute weights, extends its scope to multi-sided agent sets in complex matching, and introduces dynamic screening mechanisms to refine the matching process. This book is not just a theoretical exploration. It lays the groundwork for intelligent matching algorithms and group mechanisms, providing actionable insights for technical supply and demand allocation, emergency personnel dispatch, and multi-stage medical management scheme selection. The effectiveness of these methods is backed by comparative analyses and simulation experiments, proving their superiority in real-world applications. Embrace the future of decision-making with our book, a must-read for those seeking to master complex matching scenarios and unlock practical solutions.