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Proceedings 2018, 2(11), 636; https://doi.org/10.3390/proceedings2110636

Fuzzy Linear Regression of Rainfall-Altitude Relationship

Department of Rural and Surveying Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Presented at the 3rd EWaS International Conference on “Insights on the Water-Energy-Food Nexus”, Lefkada Island, Greece, 27–30 June 2018.
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Published: 27 August 2018
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Abstract

Classical linear regression has been used to measure the relationship between rainfall data and altitude in different meteorological stations, in order to evaluate a linear relation. The values of rainfall are supposed as dependent variables and the values of elevation of each station as independent variables. It has long been known that a classical statistical relationship exists between annual rainfall and the station elevation which in many cases is linear as the one examined in this article. However classical linear regression makes rigid assumptions about the statistical properties of the model, accepting the error terms as random variables, and the violation of this assumption could affect the validity of the classical linear regression. Fuzzy regression assumes ambiguous and imprecise parameters and data. For this reason it may be more effective than classical regression. In this paper we evaluate the relationship between annual rainfall data and the elevation of each station in Thessaly’s meteorological stations, using fuzzy linear regression with trapezoidal membership functions. In this possibilistic model the dependent measured elevations are crisp, and the independent observed rainfall values as well as the parameters of the model are fuzzy.
Keywords: fuzzy regression; trapezoidal parameters; fuzzy linear programming; possibilistic models fuzzy regression; trapezoidal parameters; fuzzy linear programming; possibilistic models
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Tzimopoulos, C.; Evangelides, C.; Vrekos, C.; Samarinas, N. Fuzzy Linear Regression of Rainfall-Altitude Relationship. Proceedings 2018, 2, 636.

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