Aggregation Theory Beyond the Unit Interval -- Formal Concept Analysis and Uncertainty -- Fuzzy Implication Functions -- Fuzzy Mathematical Analysis and its Applications -- Generalized Sets and Operators -- Information Fusion Techniques based on Aggregation Functions, Pre-aggregation Functions, and their Generalizations -- Interval Uncertainty -- Knowledge Acquisition, Representation and Reasoning -- Logical Structures of Opposition and Logical Syllogisms -- Mathematical Fuzzy Logics -- Theoretical and Applied Aspects of Imprecise Probabilities.

This two-volume set (CCIS 1601-1602) constitutes the proceedings of the 19th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2021, held in Milan, Italy, in July 2022. The 124 papers were carefully reviewed and selected from 188 submissions. The papers are organized in topical sections as follows: aggregation theory beyond the unit interval; formal concept analysis and uncertainty; fuzzy implication functions; fuzzy mathematical analysis and its applications; generalized sets and operators; information fusion techniques based on aggregation functions, pre-aggregation functions, and their generalizations; interval uncertainty; knowledge acquisition, representation and reasoning; logical structures of opposition and logical syllogisms; mathematical fuzzy logics; theoretical and applied aspects of imprecise probabilities; data science and machine learning; decision making modeling and applications; e-health; fuzzy methods in data mining and knowledge discovery; soft computing and artificia intelligence techniques in image processing; soft methods in statistics and data analysis; uncertainty, heterogeneity, reliability and explainability in AI; weak and cautious supervised learning.