In this groundbreaking work, a new axiomatic framework develops a set of fuzzy mathematical models for random phenomena. These models encompass multiple, interval, fuzzy, and any incomplete or fragmented statistical descriptions of a phenomenon's characteristics, approaching probability distributions as a limit derived from an abundance of data. The scope of these models ranges from unstable, unique events to statistically stable occurrences that can be repeated. Within these broad parameters, concepts of interval probability and averages are illuminated and interpreted, causal relationships are analyzed, random transformations are explored, and the dynamics of dependence and independence are examined. Limit laws are investigated, random processes are described, and much more. The text introduces criteria specific to these new models and develops universal methods for synthesizing optimal decision-making rules (such as estimations and hypothesis discrimination). The structures implementing these rules are designed to be simple yet effective in adapting to changing environmental conditions, grounded in the selection of reliable models. Trust in these models is built through the incorporation of a limited number of initial probabilities and averages, presented in interval form to reflect the instability of real phenomena and the scarcity of initial data. The joint synthesis of reliable models and decision-making rules is also considered. This book is essential reading for researchers in the fields of communication and control, and it will be valuable to anyone interested in mathematical methods for describing random phenomena and tackling decision-making challenges under uncertainty.