This paper focuses on the generalization of classifiers in noisy problems and aims at construction learning classifier system (LCS) that can acquire the optimal classifier subset by dynamically determining the classifier generalization criteria. In this paper, an accuracy-based LCS (XCS) that uses the mean of the reward (XCS-MR) is introduced, which can correctly identify classifiers as either accurate or inaccurate for noisy problems, and investigates its effectiveness when used for several noisy problems. Applying XCS and an XCS based on the variance of reward (XCS-VR) as the conventional LCSs, along with XCS-MR, to noisy 11-multiplexer problems where the reward value changes according to a Gaussian distribution, Cauchy distribution, and lognormal distribution revealed the following: (1) XCS-VR and XCS-MR could select the correct action for every type of reward distribution; (2) XCS-MR could appropriately generalize the classifiers with the smallest amount of data; and (3) XCS-MR could acquire the optimal classifier subset in every trial for every type of reward distribution.