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It seems there is a scope to study how we can find the fuzzy reliability of two-stage weighted-k-out-n. This paper studies the fuzzy reliability of two-stage weighted-k-out-of-n model with components in common. Algorithms are developed to calculate the system fuzzy reliability, and generate the minimal cuts and minimal paths of two-stage weighted-k-out-of-n systems. Fuzzy reliability bounds for systems with s-dependent component failures are investigated based on the generated minimal cuts and minimal paths. Two types of two-stage weighted-k-out-of-n models, the Series Weighted (SW)-k-out-of-n model, and the Parallel Weighted (PW)-k-out-of-n model, can be applied to investigate fuzzy reliability issues in network applications, such as the project management, and the shortest path problems. Examples are provided to demonstrate the developed models and algorithms of systems having components following different type of membership functions.