Mathematically Representing Hybrid Qualitative and Quantitative Solutions

Across disciplines, designing systems and solutions increasingly involves different forms of information. Resource systems, education, health care, and technological communication systems all include cyber, physical, and social elements. The interfaces between the physical system, people, and smart systems are increasingly more prevalent in everyday activities. The connections between these elements are needed in systems analysis and modeling for determining appropriate solutions. As such, the interconnectivity of Industry 4.0 has prompted the expansion of cyber-physical systems to include social elements. The evolution of cyber-physical-social (CPS) systems requires the computational foundations that support the integration of diverse types of information (qualitative and quantitative) in modeling and analysis. Furthermore, creating policies and solutions that are sustainable requires the incorporation of technical, social, environmental, economic, and political parameters. A key challenge in the development and analysis of solutions is incorporating heterogeneous parameters. Accordingly, we propose an approach that allows for determining solutions that are hybrid (qualitative, quantitative, technical, and nontechnical) in nature. By expanding the mathematics and constructs to incorporate, different types of solutions may be combined to form more suitable, holistic solutions. We propose using bond graph modeling with scenario planning for quantification to achieve this. This approach is demonstrated using a test problem in managing the well-being of a person with a treatment plan, with respect to the quality of life of the patient. The outcomes of this research are expected to support decision making in determining solutions that are multi-faceted in nature. This is particularly important in the healthcare industry, with the outcomes of healthcare treatment being qualitative in nature.