The uncertainty principle is an important principle in quantum theory. Based on this principle, it is impossible to predict the measurement outcomes of two incompatible observables, simultaneously. Uncertainty principle basically is expressed in terms of the standard deviation of the measured observables. In quantum information theory, it is shown that the uncertainty principle can be expressed by Shannons entropy. The entopic uncertainty lower bound can be altered by considering a particle as the quantum memory which is correlated with the measured particle. We assume that the quantum memory is an open system. We also select the quantum memory from $N$ qubit which interact with common reservoir. In this work we investigate the effects of the number of additional qubits in reservoir on entropic uncertainty lower bound. We conclude that the entropic uncertainty lower bound can be protected from decoherence by increasing the number of additional qubit in reservoir.
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