FCM Modeling Background User Guide — Concepts and Application

Version: 3.9.1

1 Nomenclature

Term	Definition
FCM	Fuzzy Cognitive Maps
FFP	Functional Flow Property

2 Fuzzy Cognitive Maps (FCM)

FCM is a methodology of modeling that represents a network of interconnected concepts in order to understand the network's performance. Each of the concepts in the network may be connected to other concepts through causal connections that represent the performance dependencies between the concepts. Concepts are factors in the network that may exert influence on one another through causational relationships (e.g. an increase in concept A causes a decrease in concept B). Utilizing FCM allows complex networks of interdependent concepts to be modelled. Furthermore, the impacts of changes in magnitude to one concept are simulated throughout the network.

Figure 1 ("Example of a Generic FCM Diagram") shows six concept nodes C1–C6 interconnected by directed, weighted causal connections labeled W16, W21, W23, W25, W32, W34, W36, W41, W42, W45, W51, W54, W63, illustrating an arbitrary densely-interconnected concept network.

3 Application in MADE

FCM is used in MADE to model complex engineering systems (i.e. in a "network" of items) where performance variables (concepts) of interest are defined using Functional Flow Properties (FFP).

The role of items (e.g. subsystems & components) in MADE is to act as an agent of change upon the incoming functional flows, resulting in the output of functional flows. A Functional Flow Property (FFP) enters the item via an input port. It is then processed and finally connected to an FFP, which leaves the item. The items in the MADE model are defined by their incoming and outgoing FFPs.

Figure 2 ("Network of items in a system model with connections display flow properties") shows the "Diesel Engine - System Model": IN → {Mass flow rate, Static pressure, Voltage, Amplitude} → Air Filter (Mass flow rate) / Governor (Linear velocity) / Lift Pump → Primary Fuel Filter → Secondary Fuel Filter → Injector Pump (Dynamic pressure) → Engine (Torque) → OUT, with Coupling 1 providing Angular velocity feedback into Lift Pump — flow property labels colored by category (green = material/liquid, red = energy/mechanical, blue = signal).