Research

**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.