‎why linear (and piecewise linear) models often successfully describe complex non-linear economic‎ ‎and financial phenomena‎: ‎a fuzzy-based explanation

Economic and financial phenomena are highly complex and non-linear. however, surprisingly, in many cases, these phenomena are accurately described by linear models – or, sometimes, by piecewise linear ones. in this paper, we show that fuzzy techniques can explain the unexpected efficiency of linear and piecewise linear models: namely, we show that a natural fuzzy-based precisiation of imprecise (“fuzzy”) expert knowledge often leads to linear and piecewise linear models. we show this by applying invariance ideas to analyze which membership functions, which fuzzy “and”-operations (t-norms), and which fuzzy implication operations are most appropriate for applications to economics and finance. we also discuss which expert-motivated nonlinear models should be used to get a more accurate description of economic and financial phenomena: specifically, we show that a natural next step is to add cubic terms to the linear (and piece-wise linear) expressions, and, in general, to consider polynomial (and piece-wise polynomial) dependencies.