Why Linear (and Piecewise Linear) Models Often Successfully Describe Complex Non-Linear Economic and Financial Phenomena: A~Fuzzy-Based Explanation
عنوان مقاله: Why Linear (and Piecewise Linear) Models Often Successfully Describe Complex Non-Linear Economic and Financial Phenomena: A~Fuzzy-Based Explanation
شناسه ملی مقاله: JR_TFSS-2-1_009
منتشر شده در در سال 1402
شناسه ملی مقاله: JR_TFSS-2-1_009
منتشر شده در در سال 1402
مشخصات نویسندگان مقاله:
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.
خلاصه مقاله:
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.
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.
کلمات کلیدی: Linear models, Piece-wise linear models, Fuzzy Logic, Economics and finance
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1662378/