Recently,reinforcement learning (RL) methods have been used for learning problems in environments with embedded hidden states. However, conventional RL methods have been limited to handlingMarkov decision process problems. In order to overcome hidden states, several algorithms were proposed, but these need an extreme amount of memory of past sequences which represent historical state transitions. The aim of this work was to extend our previously proposed algorithm for hidden states in an environment, calledlabeling Q-learning (LQ-learning), which reinforces incompletely observed perception by labeling. In LQ-learning, the agent has a perception structure which consists of pairs of observations and labels. From these pairs, the agent can distinguish more exactly hidden states which look the same but are actually different each other. Labeling is carried out by labeling functions. Numerous labeling functions can be considered, but here we introduce some labeling functions based on the sequence of only the last and the current observations. This extended LQ-learning is applied to grid-world problems which have hidden states. The results of these simulations show the availability of LQ-learning.