Coupling Mechanistic Approaches and Fuzzy Logic to Model and Simulate Complex Systems

Several mathematical formalisms can be exploited to model complex systems, in order to capture different features of their dynamic behavior and leverage any available quantitative or qualitative data. Correspondingly, either quantitative models or qualitative models can be defined; bridging the gap between these two worlds would allow us to simultaneously exploit the peculiar advantages provided by each modeling approach. However, to date, the attempts in this direction have been limited to specific fields of research. In this paper, we propose a novel, general-purpose computational framework, named Fuzzy-mechanistic modeling of compleX systems (FuzzX), for the analysis of hybrid models consisting of a quantitative (or mechanistic) module and a qualitative module that can reciprocally control each other's dynamic behavior through a common interface. FuzzX takes advantage of precise quantitative information about the system through the definition and simulation of the mechanistic module. At the same time, it describes the behavior of components and their interactions that are not known in full details, by exploiting fuzzy logic for the definition of the qualitative module. We applied FuzzX for the analysis of a hybrid model of a complex biochemical system, characterized by the presence of positive and negative feedback regulations. We show that FuzzX is able to correctly reproduce known emergent behaviors of this system in normal and perturbed conditions. We envision that FuzzX could be employed to analyze any kind of complex system when quantitative information is limited, as well as to extend existing mechanistic models with fuzzy modules to describe those components and interactions of the system that are not fully characterized.