Affiliations: [a] Department of Rural and Surveying Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece | [b] Department of Mathematics, Kuwait University, Khaldiya Campus, Safat, Kuwait
Correspondence:
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Corresponding author: Christos Tzimopoulos, Department of Rural and Surveying Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece. E-mail: ctzimop@gmail.com.
Abstract: In this article, we examine the solution of the fuzzy linear absorption equation, which represents the water movement in a horizontal column and describes the wetting up of the column under tension. The equation describing the problem is a fuzzy partial differential parabolic equation (diffusion) of second order. The calculation of water flow in the unsaturated zone requires the knowledge of the initial and boundaries conditions as well as the various soil parameters. But these parameters are subject to different kinds of uncertainty due to human and machine imprecision. For that reason fuzzy set theory was used for facing imprecision or vagueness. As the problem concerns fuzzy differential equations, the generalized Hukuhara (gH) derivative was used for total derivatives, as well as the extension of this theory for partial derivatives. The results are the fuzzy moisture contents versus time and the fuzzy cumulative infiltration as well the infiltration rate versus time.
