Domain adaptation aims to leverage knowledge acquired from a related domain (called a source domain) to improve the efficiency of completing a prediction task (classification or regression) in the current domain (called the target domain), which has a different probability distribution from the source domain. Although domain adaptation has been widely studied, most existing research has focused on homogeneous domain adaptation, where both domains have identical feature spaces. Recently, a new challenge proposed in this area is heterogeneous domain adaptation where both the probability distributions and the feature spaces are different. Moreover, in both homogeneous and heterogeneous domain adaptation, the greatest efforts and major achievements have been made with classification tasks, while successful solutions for tackling regression problems are limited. This paper proposes two innovative fuzzy rule-based methods to deal with regression problems. The first method, called fuzzy homogeneous domain adaptation, handles homogeneous spaces while the second method, called fuzzy heterogeneous domain adaptation, handles heterogeneous spaces. Fuzzy rules are first generated from the source domain through a learning process; these rules, also known as knowledge, are then transferred to the target domain by establishing a latent feature space to minimize the gap between the feature spaces of the two domains. Through experiments on synthetic datasets, we demonstrate the effectiveness of both methods and discuss the impact of some of the significant parameters that affect performance. Experiments on real-world datasets also show that the proposed methods improve the performance of the target model over an existing source model or a model built using a small amount of target data.
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