Particle swarm optimization for determining fuzzy measures from data

Fuzzy measures and fuzzy integrals have been successfully used in many real applications. How to determine fuzzy measures is the most difficult problem in these applications. Though there have existed some methodologies for solving this problem, such as genetic algorithms, gradient descent algorithms and neural networks, it is hard to say which one is more appropriate and more feasible. Each method has its advantages and limitations. Therefore it is necessary to develop new methods or techniques to learn distinct fuzzy measures. In this paper, we make the first attempt to design a special particle swarm algorithm to determine a type of general fuzzy measures from data, and demonstrate that the algorithm is effective and efficient. Furthermore we extend this algorithm to identify and revise other types of fuzzy measures. To test our algorithms, we compare them with the basic particle swarm algorithms, gradient descent algorithms and genetic algorithms in literatures. In addition, for verifying whether our algorithms are robust in noisy-situations, a number of numerical experiments are conducted. Theoretical analysis and experimental results show that, for determining fuzzy measures, the particle swarm optimization is feasible and has a better performance than the existing genetic algorithms and gradient descent algorithms.