Equationless and equation-based trend models of prohibitively complex technological and related forecasts

- Qualitative quantifiers are - positive, zero, negative.
- Positive qualitative constant A is irrelevant; AX = (+)X = X.
- Qualitative interactions of three technologies are studied.
- Set of three qualitative differential equations gives 463 solutions/scenarios.
- Qualitative heuristics give 79 scenarios and 396 time transitions among them.

PCF (Prohibitively Complex Forecast) models integrate several aspects, e.g. macroeconomic, ecology, sociology, engineering and politics. They are unique, partially subjective, inconsistent, vague and multidimensional. PCFs development suffers from IS (Information Shortage). IS eliminates straightforward application of traditional statistical methods. Oversimplified or highly specific PCFs are sometimes obtained. Artificial Intelligence has developed different tools to solve such problems. Qualitative reasoning is one of them. It is based on the least information intensive quantifiers i.e. trends. There are four different trends i.e. qualitative values and their derivatives: plus/increasing; zero/constant; negative/decreasing; any value/any trend. The paper studies PCF models represented by a set of NODE (nonlinear ordinary differential equations) and models based on EHE (equationless heuristics). An example of EHE is - if GDP is increasing then Research and Development investment is increasing more and more rapidly. Such verbal knowledge item cannot be incorporated into a traditional numerical model and a qualitative model must be used. The following qualitative equation eliminates all positive multiplicative constants A from PCF NODE models: AX = (+)X = X. Numerical values of NODEs constants are therefore qualitatively irrelevant. A solution of a qualitative model is represented by a set of scenarios and a set of time transitions among these scenarios. A qualitative model can be developed under conditions when the relevant quantitative PCF must be heavily simplified. The key information input into PCF EHE model is expert knowledge. A consensus among experts is often not reached because of substantial subjectivity of experts' knowledge. The case study analyses interactions of three technologies using modified predator/prey model. It is based on three NODEs and three EHEs. NODEs have 463 scenarios and EHEs has 79 scenarios. The results are given in details. No a prior knowledge of the qualitative model theory is required.