Irstea Montpellier, bâtiment Minéa, salle Orient
Fuzzy identification with complex usage of the criteria of accuracy, compactness, transparency and interpretability
par Serhiy Shtovba, Professor with the Computer Science Department, Vinnytsia Technical University, Ukraine
Abstract: Identification of nonlinear dependences, i.e., the construction of their mathematical models from the results of observations, is an important problem and finds use in engineering, economy, medicine, sociology, agriculture, environmental, and other domains. We consider a fuzzy identification which produces fuzzy models, especially the models in form of fuzzy rule bases. We discuss 3 types of fuzzy models: with crisp numerical output, with discrete output (classifier), and with fuzzy output.
It is most simple to identify quality of fuzzy identification with accuracy, i.e. with deviation of the fuzzy inference results from the experimental data. This approach, which dominates in the modern theory of fuzzy identification, has led to a number of negative results. Since 1990s a race for “accuracy” has started in the fuzzy scientific community, which resulted in elaboration of a number of methods for designing highly accurate fuzzy rule bases. However, fuzzy rule bases developed in accordance with these methods have lost a significant competitive advantage – the ability to describe the dependence under study with literally few natural-language statements understandable to the customers – experts in the applied areas without specialized mathematical qualification. Customers perceive such highly accurate fuzzy rule bases as an incomprehensible set of numbers that they are not used to trust when making important decisions. Thus, in addition to accuracy, other quality criteria of fuzzy rule base should be taken into account while solving applied fuzzy identification problems. The following particular criteria of fuzzy identification quality are disused: accuracy, compactness, transparency, and interpretability. Also, we propose the multicriterial methods for ensuring the desired quality of fuzzy identification of multifactor dependences.