8.1. Isomorphism

We use the following terminology to connect choosing, modeling, and systems thinking. In this terminology the isomorphism between designing, choosing, modeling and systems thinking are crucial. This is important to be able to connect mathematical systems to design systems to choice systems in a congruent way.
This gives us the basis for the correspondence rules between these kinds of systems.

We define the optimal design as the particular configuration of characteristics of a new object that meets the aims of all actors involved in the design process best and does not violate any (physical) limitations.

We define the optimal choice as the alternative having the highest overall preference (which is a function of weights attached to criteria and preference ratings attached to alternatives by decision makers) and meets all veto-criteria.

We define the optimal solution as the vector of variables that, given the objective function and subject to constraints, cannot be improved.

Finally, we define the optimal system state as the set of relevant properties of that system that, given the system’s goal and subject to the system’s environment, cannot be improved.

Using the above definitions, we can distinguish parallel terminology across these fields of inquiry as shown in the next table.

Designing	Decision making	Optimization	Systems thinking
Optimal design	Optimal choice	Optimal solution	Optimal system state
Configuration of characteristics	Alternative performance on all criteria	Vector of variables	Set of relevant properties
Aims of all actors	Overall preference score	Objective function	Goal/output
Limitations	Veto-criteria	Constraints	Environment