Backward rough-fuzzy rule interpolation

Fuzzy rule interpolation is an important technique for performing inference with sparse rule bases. Even when a given observation has no overlap with the antecedent values of any existing rules, fuzzy rule interpolation may still derive a conclusion. In particular, the recently proposed rough-fuzzy rule interpolation offers greater flexibility in handling different levels of uncertainty that may be present in sparse rule bases and observations. Nevertheless, in practical applications with inter-connected subsets of rules, situations may arise where a crucial antecedent of observation is absent, either due to human error or difficulty in obtaining data, while the associated conclusion may be derived according to alternative rules or even observed directly. If such missing antecedents were involved in the subsequent interpolation process, the final conclusion would not be deduced using a forward rule interpolation technique alone. However, missing antecedents may be related to certain intermediate conclusions and therefore, may be interpolated us- ing the known antecedents and these conclusions. Following this idea, a novel backward rough-fuzzy rule interpolation approach is proposed in this paper, allowing missing observations which are indirectly related to the final conclusion to be interpolated from the known antecedents and intermediate conclusions. As illustrated experimentally, the resulting backward rough-fuzzy rule interpolation system is able to deal with uncertainty, in both data and knowledge, with more flexibility.