Fuzzy Compositional Modeling

Automated modeling refers to automatic (re-)formulation of alternative system models that embody the simplification, abstraction, and approximation of knowledge and data for a given task. This technique is highly desirable for effective problem solving in many application domains. Over the past two decades, compositional modeling (CM) has established itself as a leading approach in automated modeling. CM is a framework to construct system models by composing generic and reusable model fragments (MFs) selected from a knowledge base. However, the existing work mainly concerns the knowledge and data that are represented by crisp and precise information. Little work has been carried out to explore its potential to deal with uncertain environments. This paper presents an innovative framework of fuzzy compositional modeling (FCM) to develop such work. The proposed approach is capable of representing and reasoning with a wide range of inexact information. An innovative notion of fuzzy complex numbers (FCNs) is developed in an effort to enable synthesis of consistent scenario descriptions from imprecise MFs. This paper also introduces the modulus of FCNs to constrain the resulting scenario descriptions. The usefulness of this study is illustrated by means of an example to construct possible scenario descriptions from given evidence, which is in support of crime investigation.