This book is an in-depth study of the application of Linguistic Z numbers in various domains. It is divided into 18 chapters, each focusing on different aspects and applications of Linguistic Z numbers. The first chapter introduces the concept of a Linguistic Z number fuzzy probabilistic rough set and their corresponding three-way decisions. The second chapter discusses the TOPSIS-based multi-attribute group decision-making (MAGDM) under Linguistic Z number information. The third chapter presents a new approach of multi-criteria group decision-making (MCGDM): MARCOS-based alternatives measurement with ranking under Linguistic Z number information and their application in the selection of logistics distribution cold chain center. The fourth chapter focuses on the Linguistic Z number environment-based site selection of medical logistic centers with the TODIM-VIKOR approach. The fifth chapter explores MCGDM based on TODIM-PROMETHEE II under Linguistic Z number environment and their application in site selection of emergency shelters. The sixth chapter introduces a novel approach of extended ORESTE-based Linguistic Z number MAGDM and their applications in the ability of regional energy assessment. The seventh chapter discusses MCGDM based on MULTIMOORA with Linguistic Z number and their application in software selection. The eighth chapter presents multi-criteria group decision-making using the LogTODIM-TOPSIS approach in a Linguistic Z number environment for selecting auto parts materials in the technology of automobiles. The ninth chapter introduces a Linguistic Z number CoCoSo approach for multi-criteria group decision-making and application to the diagnosis of sepsis. The tenth chapter discusses The ExpTODIM-VIKOR approach under a Linguistic Z number environment and its applications to solve multi-criteria group decision-making problems. This book provides a deep understanding of Linguistic Z numbers and their applications in decision-making, granular computing, and social networks. It is a valuable resource for researchers and practitioners in these fields.