We consider function approximation by fuzzy systems. Fuzzy systems are typically used for approximating deterministic functions, in which the stochastic uncertainty is ignored. We propose probabilistic fuzzy systems in which the probabilistic nature of uncertainty is taken into account. Furthermore, these systems take also fuzzy uncertainty into account by their fuzzy partitioning of input and output spaces. We discuss an additive reasoning scheme for probabilistic fuzzy systems that leads to the estimation of conditional probability densities, and prove how such fuzzy systems compute the expected value of this conditional density function. We show that some of the most commonly used fuzzy systems can compute the same expected output value and we derive how their parameters should be selected in order to achieve this goal.

Additional Metadata
Keywords additive reasoning, function approximation, fuzzy partitioning, fuzzy set, probabilistic fuzzy system
Publisher Erasmus Research Institute of Management (ERIM)
Persistent URL hdl.handle.net/1765/30923
van den Berg, J, Kaymak, U, & Almeida e Santos Nogueira, R.J. (2011). Function Approximation Using Probabilistic Fuzzy Systems (No. ERS-2011-026-LIS). ERIM Report Series Research in Management. Erasmus Research Institute of Management (ERIM). Retrieved from http://hdl.handle.net/1765/30923