Fuzzy Learning Algorithms


Fuzzy set theory provides a theoretical foundation for modeling complex systems in which only an imprecise or approximate description of the relationships among the components of the system is available. The focus of an ongoing research project is the development and analysis of algorithms to generate fuzzy rule bases from training data. The research has produced a hierarchical architecture and learning strategy that generates more precise models with fewer training instances. The hierarchical architecture has been shown to be suitable for adaptive models.


Current efforts focus on the refinement of fuzzy rule-based models and learning algorithms. Areas of research include rule reduction to enhance interpretability, combining models, data fusion and domain decomposition techniques, and the analyzing the effects of granularity and generalizability in fuzzy systems.



Modeling and Complexity


Fuzzy set theory, neural networks, and genetic algorithms are three soft computing disciplines that are suited for learning system models or function approximations from training data. As the systems being modeled have increased in complexity, the number of variables required to describe the state of the system has increased accordingly. The additional sophistication introduces the problem of scaling into the construction of models: Will the techniques that have been employed in construction models with few inputs continue to be successful in domains with multiple inputs?


An ongoing area of research is the analysis of the robustness of soft computing algorithms by analyzing the effects of increasing complexity on the performance of the resulting models and learning algorithms themselves. The overall objective is to enhance the robustness of the learning process by the development of hybrid algorithms that employ techniques from several soft computing disciplines.



Similarity, Analogy, and Inference


The assessment of the similarity of objects provides the foundation for reasoning by analogy and interpolation. Similarity is frequently measured using set-theoretic operations or metric properties of the underlying domain. An objective of this project is to categorize similarity measures by their applicability for use in analogical and interpolative reasoning.


A methodology based on metric similarity has been introduced to facilitate inference in sparse databases using fuzzy rules. The technique uses proximity to extend the information contained in the rules from a set of paradigmatic examples to the entire domain.