DEVELOPMENT OF A FUZZY CALCULATOR FOR CONTINUOUS FUNCTIONS OF NON-INTERACTIVE FUZZY VARIABLES

摘要

The goal of this paper is to develop a Fuzzy Calculator, making it possible to calculate functions of fuzzy intervals, as prescribed by the extension principle of Zadeh. The extension principle can be reversed, resulting in fixed α-levels for which the minimum and the maximum of the function has to be determined. This optimization problem can be tackled by different algorithms: Gradient Descent, SIMPSA, Particle Swarm Optimization and Particle Swarm optimization in combination with Gradient Descent. Two approaches are used to determine the number of α-levels: it is either fixed to a predetermined value, or it is initially chosen very small and subsequently expanded according to a suitable criterion. Both a non-parallel and a parallel implementation of the Fuzzy Calculator are designed. In the parallel version, communication is used to optimize the internal workings of PSO. The Fuzzy Calculator is applied to a number of test functions. The different combinations of optimization algorithms are evaluated, both by the final result and by the number of required model evaluations. The results indicate that the parallel implementation of the Fuzzy Calculator starting with a small number of α-levels and using PSO with Gradient Descent leads to the most accurate membership function.