Validation

The central theme of my research interest is validation implemented by computers. When a computer returns a solution, how does one know (with mathematical certainty) whether or not the solution is valid?

Uncertainty

How is it possible to explicitly model error and uncertainty in mathematical analyses? There are methods of interval analysis, probability, possibility theory, and simultaneous (fuzzy) set theory. Of these methods, those that I find compelling are interval analysis and simultaneous set theory.

Optimization

• Linear and nonlinear programming
• Fuzzy linear programming
• Feasibility set analysis – redundant and inconsistent systems
• Optimal Control

Differential Algebraic Equations

• Validated numerical methods for solving differential equations
• Application of differential equations to unconstrained optimal control

Geographical Information Systems

• Uncertainty and error propagation
• Error analysis in suitability and overlay analyses

• Radiation of tumors
• Radiosurgery

Environment

• Food production
• Pesticide and herbicide pollution models
• Hazard analysis

• Scheduling – fuzzy scheduling