Why Linear (and Piecewise Linear) Models Often Successfully Describe Complex Non-Linear Economic and Financial Phenomena: A~Fuzzy-Based Explanation
Publish place: Transactions on Fuzzy Sets and Systems، Vol: 2، Issue: 1
Publish Year: 1402
نوع سند: مقاله ژورنالی
زبان: English
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JR_TFSS-2-1_009
تاریخ نمایه سازی: 2 خرداد 1402
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.
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Authors
Hung Nguyen
Department of Mathematical Sciences, New Mexico State University, Las Cruce, New Mexico, USA. and Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand.
Vladik Kreinovich
Department of Computer Science, University of Texas at El Paso, El Paso, Texas, USA.
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