This paper proposes a novel Learning Classifier System (LCS) called Identification-based LCS (IXCS) to promote a generalization of classifiers (i.e., rules) by selecting effective ones and deleting ineffective ones. Through the intensive simulation of the 20-Multiplexer problem, this paper has revealed the following implications which cannot be achieved by the conventional LCS, XCSTS: (1) IXCS can not only generalize the classifiers earlier but also generate the classifiers which are robust to the noisy environment; and (2) IXCS can derive a higher performance with a lower number of micro-classifiers.