Learning Classifier Systems (LCSs) are rule-based systems that automatically build their rule set so as to get optimal policies through evolutionary processes. This paper considers an evolutionary multi-objective optimization-based constructive method for LCSs that adjust to non-Markov environments. Our goal is to construct a XCSMH (eXtended Classifier System - Memory Hierarchic) that can obtain not only optimal policies but also highly generalized rule sets. Results of numerical experiments show that the proposed method is superior to an existing method with respect to the generality of the obtained rule sets.