Possibility Theory and Possibilistic Logic: Tools for Reasoning Under and About Incomplete Information

Dubois, Didier; Prade, Henri

doi:10.1007/978-3-030-74826-5_7

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Possibility Theory1

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2023

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“…Definition 13. A probability distribution p and a possibility distribution π are said to be consistent only if π(u) ≥ p(u), ∀u [65][66][67][68].…”

Section: Possibility Theorymentioning

confidence: 99%

Fuzzy Analytical Solution of Horizontal Diffusion Equation into the Vadose Zone

et al. 2023

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The process of how soil moisture profiles evolve into the soil and reach the root zone could be estimated by solving the appropriate strong nonlinear Richards’ equation. The nonlinearity of the equation occurs because diffusivity D is generally an exponential function of water content. In this work, the boundary conditions of the physical problem are considered fuzzy for various reasons (e.g., machine impression, human errors, etc.), and the overall problem is encountered with a new approximate fuzzy analytical solution, leading to a system of crisp boundary value problems. According to the results, the proposed fuzzy analytical solution is in close agreement with Philip’s semi-analytical method, which is used as a reference solution, after testing 12 different types of soils. Additionally, possibility theory is applied, enabling the decision-makers to take meaningful actions and gain knowledge of various soil and hydraulic properties (e.g., sorptivity, infiltration, etc.) for rational and productive engineering studies (e.g., irrigation systems).

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“…Definition 13. A probability distribution p and a possibility distribution π are said to be consistent only if π(u) ≥ p(u), ∀u [65][66][67][68].…”

Section: Possibility Theorymentioning

confidence: 99%