An Outline of Our Research

During the last two decades, the literature is flooded with the studies applying computational intelligence (i.e. numerical methods for implementing an intelligent behavior) to understand the complex and uncertain behavior of real-world processes. Despite an increased research interest in neuro/fuzzy modeling techniques, the field lacks a mathematical framework for the design and analysis of intelligent systems taking into account the underlying uncertainties in a sensible way to deal with the real-world problems. We propose, with applications to environmental science, medicine, chemistry and drug design, a modeling framework offering the possibilities of

# the design of a fuzzy filter, based on different mathematical criteria, for filtering out the uncertainties from the modeling problem;

# a mathematical analysis of the filltering methods with emphasis on stability, robustness, and steady-state error issues;

# utilizing the data about uncertainties provided by the fuzzy filter for an understanding of the process behavior.

Our investigations have shown that the standard neuro/fuzzy modeling techniques fail in many modeling problems to describe the process behavior. And the proposed modeling approach could potentially solve these complex and uncertain problems. The studies on several application examples related to the life science have verified the feasibility of our approach.

The research goal is to develop a computational paradigm that contributes to the research area "Intelligent Fuzzy Computing'' with applications in life sciences. A computational framework, that implements an "intelligent'' behavior in the sense of handling uncertainties associated to the modeling and optimization problems related to life sciences, is suggested. The proposed framework has the following salient features.

# It offers the possibility of studying (i.e. design and analysis) the fuzzy expert systems (built for modeling and optimization applications in life sciences) with the concepts of modern system theory.

# It offers the possibility of applying the mathematical tools available from probability theory in the design of fuzzy systems for dealing with the data uncertainties and many other issues.

# The framework introduces the new computational algorithms, referred to as stationary fuzzy Fokker-Planck learning (SFFPL) algorithms, based on the fusion of different concepts coming from the areas of statistical mechanics, optimization theory, and fuzzy modeling.

# Some of the analytically intractable problems related to fuzzy modeling of life science processes can be solved numerically by applying SFFPL based computational algorithms.

# The SFFPL based computational algorithms can be used for solving deterministic as well as stochastic optimization problems.

Such an intelligent computational paradigm for deterministic as well as stochastic modeling and optimization will obviously be of great use in life sciences. Several practical problems from life science are considered as applications of the developed computational algorithms.

Research Applications in Life Science