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A unique uncertainty model can not deal with an uncertain phenomenon that is changing and dynamic. For instance, the weather tomorrow will be %60 rainy. But as we see, this %60 is changing from time to time and can not be unique. In other words, there is imprecision in the weather uncertainty model. In this dissertation, we consider four advanced uncertainty models called imprecise uncertainty. These advanced uncertainty models could take into account the imprecision. Therefore, further planning, decision making, or designing under imprecision can be more optimal and stable. We applied these models to a general linear programming (LP) problem with the presence of (imprecise) uncertainty, i.e., at least one of the elements of the coefficient matrices in the constraints and/or coefficients of goal function is uncertain. We discussed four different uncertainty models: interval, possibility, contamination, and probability box models, to deal with imprecise uncertainty. We focused on imprecise probability theory to measure these uncertainties. We work on the four types of uncertainty models to quantify and solve the LPUU problem. Two sorts of theoretical solutions were proposed under the optimal decision criteria (the worst-case scenario and the maximality/less conservative criterion). We proposed a generic approach to reason about the LP problem under imprecise uncertainty. This approach is based on the imprecise decision theory. Several numerical methods in each of these eight theoretical solutions are proposed under approximation theory. In interval, contamination, and possibility distribution cases, the exact solutions are provided with novel ideas. Several applications on four real industrial/engineering problems are presented to illustrate the potentially broad domains, wide application, and highly innovative results.