Why Linear (and Piecewise Linear) Models Often Successfully Describe Complex Non-Linear Economic and Financial Phenomena: A~Fuzzy-Based Explanation
Author(s):
Article Type:
Research/Original Article (بدون رتبه معتبر)
Abstract:
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.
Keywords:
Language:
English
Published:
Transactions on Fuzzy Sets and Systems, Volume:2 Issue: 1, Spring - Summer 2023
Pages:
147 to 157
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