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Why Linear (and Piecewise Linear) Models Often Successfully Describe Complex Non-Linear Economic and Financial Phenomena: A~Fuzzy-Based Explanation | ||
Transactions on Fuzzy Sets and Systems | ||
مقاله 10، دوره 2، شماره 1، مرداد 2023، صفحه 147-157 اصل مقاله (241.35 K) | ||
نوع مقاله: Original Article | ||
شناسه دیجیتال (DOI): 10.30495/tfss.2023.1972564.1054 | ||
نویسندگان | ||
Hung T. Nguyen1؛ Vladik Kreinovich* 2 | ||
1Department of Mathematical Sciences, New Mexico State University, Las Cruce, New Mexico, USA. and Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand. | ||
2Department of Computer Science, University of Texas at El Paso, El Paso, Texas, USA. | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
Linear models؛ Piece-wise linear models؛ Fuzzy logic؛ Economics and finance | ||
مراجع | ||
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