Current
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.