Criteria for linguistic improvement of precise fuzzy models by ortliogonail transforms. Application to ART based models

The aim of this paper is focused on fuzzy models and simplification-interpretability ideas to generate simpler and more interpretable models in accordance with fuzzy logic. These concepts are not very common in (precise) fuzzy modeling methods, which are the most common approach in technical fields. Here, orthogonal transforms are considered for achieving this aim, defining a criteria set to guide the choice of an adequate rule set for the simplification procedure. Data-driven fuzzy modeling generates models with a good accuracy but other aspects about the fuzzy logic, such as compactness or interpretability, are not considered, so these models can contain an excessive number of rules, introducing redundancy, incoherence or extra fuzzy sets. In this context, the simplification-improvement procedure is carried out to try to keep most of the advantages of the original model (accuracy) while improving other aspects with poor performance: compactness, distiguishability, etc. In this way, a two step methodology is used: first, a (precise or linguistic) fuzzy algorithm for modeling is used, taking advantage of any well-known algorithm, then rule based models generated by them are improved using the criteria based on the orthogonal transforms proposed in this paper. The proposal is applied to fuzzy models generated by FasArt (Fuzzy Adaptive System ART based), this has the common drawbacks of precise fuzzy modeling. Two case-studies are considered: a DC motor and the Box-Jenkins gas furnace. For each case, two models have been generated with different complexities and fuzzy natures, then the simplification process based on orthogonal transformation is carried out by the criteria proposed, evaluating each criterion and obtaining simpler and more interpretable but sufficiently accurate fuzzy models. Here Mamdani fuzzy systems have been taken into account.