A Qualitative Simulation Framework in Smalltalk Based on Fuzzy Arithmetic

Abstract

For many systems, it is not practical to collect and correlate empirical data necessary to formulate a mathematical model. However, it is often sufficient to predict qualitative dynamics effects (as opposed to system quantities), especially for research purposes. In this effort, an object-oriented application framework (AF) was developed for the qualitative modeling of natural-resources systems. An application framework is a collection of reusable object classes that provide basic functionality for a class of applications. The user creates subclasses that inherit this functionality, and that are specific to his or her application. Smalltalk, an object-oriented programming (OOP) language, was chosen for the AF. The modeling methodology is based on Schmoldt (1991). Parameters represent variables of interest in the model system. The magnitude of a parameter is represented by its quantity, a fuzzy number, and the effects of changes in parameters upon one another are simulated over time by fuzzy arithmetic. The values of the changes in parameters and their quantities are then translated into linguistic values. The AF includes classes providing all the functionality for constructing application-specific fuzzy simulation, including FuzzyNumber, Parameter, FuzzySimulation and FuzzyTimer. Also included are data-structures such as KeyValueList and AssociationList, and modifications to Smalltalk to smoothly integrate fuzzy arithmetic for non-fuzzy values. The framework runs under Microsoft Windows 3.1, and includes a graphical user interface. In this paper, we present the AF along with an example simulation of plant physiology.

Citation

Olson, Richard L.; Schmoldt, Daniel L.; Peterson, David L. 1996. A Qualitative Simulation Framework in Smalltalk Based on Fuzzy Arithmetic. Proceedings, Statistics, Mathematics and Computers. IUFRO XX World Congress. 189-200.