Chung, Won SangAlgin, Abdullah2025-01-062025-01-0620200960-07791873-288710.1016/j.chaos.2020.1100202-s2.0-85087610181https://doi.org/10.1016/j.chaos.2020.110020https://hdl.handle.net/20.500.14669/2440In this work, we present an approach to describe imprecise probability through an effective probability theory, called the f-probability. We develop a bijective and monotonous map from the precise probability in order to construct the f-probability theory based on the f -addition, f-subtraction, f-multiplication and f-division. We apply the f-probability to the Bernoulli trial and derive the f-binomial distribution. Finally, we obtain the non-extensive entropy through the f-probability theory, and give its statistical physical implications on several areas of potential applications. PACS number(s): 02.50.Cw, 05.20.-y; 05.90.+m (C) 2020 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/closedAccessFoundations of probabilityImprecise probabilitiesUncertainty measuresNon-extensivityDeformed calculusComplex systemsNon-linear dynamicsArticleQ1139WOS:000588433800027Q1