On foundations and applications of similarity measures in case-based and rule-based reasoning

In the field of case-based and rule-based reasoning in artificial intelligence, the general formal derivation of so-called similarity measures is still an unresolved open question. In this work the theoretical framework of dimensional analysis is used to derive appropriate similarity measures for a case-based and rule-based reasoning technique. For the subclass of case descriptions in engineering design consisting of real-valued quantities with physical units it is shown how the Pi-Theorem of Buckingham can be used to construct similarity measures from these case descriptions. The necessary functional model assumptions are defined and the theoretical foundations are discussed. Within this functional model approach a proof for the correctness of the case-based and rule-based reasoning technique can be derived. An application of the case-based reasoning technique based on dimensionless groups is demonstrated using the reasoning on power efficiency in gas turbines and is compared to a conventional approach using a Voronoi-technique.