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Abstract
Fuzzy rule-based systems are widely applied for real-world decision support, such as policy formation, public health analysis, medical diagnosis, and risk assessment. However, they face significant challenges when the application problem at hand suffers from the “curse of dimensionality” or “sparse knowledge base”. Combination of hierarchical fuzzy rule models and fuzzy rule interpolation offers a potentially efficient and effective approach to dealing with both of these issues simultaneously. In particular, backward fuzzy rule interpolation (B-FRI) facilitates approximate reasoning to be performed given a sparse rule base where rules do not fully cover all observations or the observations are not complete, missing antecedent values in certain available rules. This paper presents a hierarchical bidirectional fuzzy reasoning mechanism by integrating hierarchical rule structures and forward/backward rule interpolation. A computational method is proposed, building on the resulting hierarchical bidirectional fuzzy interpolation to maintain consistency in sparse fuzzy rule bases. The proposed techniques are utilised to address a range of decision support problems, successfully demonstrating their efficacy.
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