This chapter presents the mathematical formulation of the fuzzy logic-based inference systems, used as means to infer about the response of ill-conditioned systems, based on the field knowledge representation in the fuzzy world. Particular approaches are explored, e.g., Fuzzy Inference System (FIS), Adaptive Networks-based FIS (ANFIS), Intuitionistic FIS (IFIS) and Fuzzy Cognitive Map (FCM), surfacing their potentialities in modeling applications, such as those in the field of learning, examined in the chapters of Part III that follow.