Several mechanisms like Deep Quantum Machine Learning and Artifical Neural Networks (ANN) are available for modeling real-life phenomena having complete data set. But there are certain real-life situations where the modeling is possible only by applying fuzzy logic on the available incomplete and ambiguous data. The examples like illegal migration and human trafficking need directed fuzzy graph models with additional illegal path compo-nents. In this article, we develop the theory of directed fuzzy incidence graphs (DFIG), that aid in the analysis of a number of dynamic networks. The relations found in DFIGs are asymmetric, so that the extent of node-arc interactions can be well studied. In this work, we take a different approach to connectivity by focusing legal and illegal flows through the network. In addition, we study the concepts of cycles and characterize some special type of nodes, arcs, and d-pairs in DFIGs. Also, we examine the migration of refugees across Mexico and the U. S as an application.(c) 2022 Elsevier Inc. All rights reserved.
