The Role of Uncertainty Principles in Inductive Systems Modelling

It is well known that the only way of making complexity in inductive (data‐driven) systems modelling manageable is to be tolerant of predictive (or retrodictive) uncertainty in the resulting models. It is argued that two complementary principles — the principles of maximum and minimum uncertainty — are essential to using uncertainty properly to combat complexity. When uncertainty is conceptualised in terms of probability theory, these principles become the well‐established principles of maximum and minimum entropy. When a more general framework of fuzzy measures is employed, uncertainty becomes a multi‐dimensional entity and the maximum and minimum uncertainty principles lead to optimisation problems with multiple objective criteria. Four distinct types of uncertainty are now recognised and their well‐justified measures determined within fuzzy set theory and one subset of fuzzy measures — the Dempster‐Shafer theory of evidence. The uncertainty types and their measures are briefly described.