Modelling the Mathematical Behaviour of a Computerized Hierarchical Questionnaire

We present a prototype model enabling us to study the mathematical behaviour of a computerized hierarchical questionnaire. Besides its hierarchical structure, the latter has the following characteristics: i) a closed set of pre-determined acceptable answers is associated to every question, and ii) the questionnaire should return a certain numerical outcome based on the answers, each of these being associated with a numerical weight. The model uses a program called a results generator, which generates all possible results; thus the requirement to have a finite number of possible answers. The generator transforms the questionnaire into a mega-decision tree to process every possible result from which we derive a curve. From that curve (a depiction of a mathematical function), we propose a way to interpret the results. The model is applied to a real-life computerized hierarchical questionnaire to demonstrate its capabilities.