Modeling with Uncertainty – Interval Computations Using Fuzzy Sets

A new method of interval computations using fuzzy sets and stochastic processes is proposed. It is concerned with the development of a practical technology that can be used by engineers and researchers to facilitate the process of decision making under uncertainty, in a state of “bounded rationality”. The methodology called Interval Resolution considers a model and interval values specified by the researcher for each model parameter of interest, and returns the feasible interval ranges for all model’s parameters. The process continues with the researcher refocusing on different subsets of parameters as needed and can end up with collapsing some intervals. Fuzzy sets and Monte Carlo methods are used to compute the feasible ranges. A modeling software, Interval Solver, and a descriptive langua ge are proposed and implemented along with the IR Integrated Development Environment. A number of applications have been considered. Theoretical and experimental analysis of computational efficiency is under way.