الفهرس 
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Abstract
Many real-life applications are modeled as mathematical programming problems. Most of these have many uncertain variables. Supply chain (SC) is one of these real-life problems with uncertain decision-making variables. SC linear programming model employs to minimize the total transportation costs between elements of Supply chain management (SCM). SC works in an uncertain environment like customer demand, supply deliveries and market supply. Mathematical tools are not always efficient to represent uncertainty in these systems. The fuzzy sets, rough sets and rough-fuzzy sets are efficient for solving SC problem. This thesis considers representing uncertainty in supply chain using three different approaches: fuzzy sets, rough sets and rough-fuzzy systems representation. This was applied in two real data industrial case studies: automotive manufacturing system and an edible vegetable oils manufacturer. Fuzzy sets constitute a powerful tool for handling uncertainty. The proposed fuzzy linear programming(FLP) model exhibits greater computational efficiency and flexibility by adopting the linear membership functions and distributions for solving the fuzzy SC network problems. But, Rough set theory is able to provide more insights into the true perceptions of customers. The proposed rough model can be used to identify the priorities of customer needs. Two case studies were used to evaluate the two proposed models. Rough set theory can be overlapped with many other theories, especially with fuzzy set theory; that is called the proposed rough-fuzzy model. This can be viewed in its own rights, as an independent, complementary, and not competing discipline.
Finally, comparison between fuzzy set and rough set optimization results under uncertainty is presented. Rough set are used to give a better optimization based on better accurate mathematical models. Rough-fuzzy set proved to be convenient for decision makers giving a wide optimized performance range. The results revealed a clear enhancement in optimization.
Keywords: - Rough set; Fuzzy set; Uncertainty; Fuzzy number; Rough-Fuzzy; Supply chain management (SCM)