Probabilistic Reasoning in Fuzzy Rule-Based Systems

Abstract

We concentrate on Takagi—Sugeno (TS) probabilistic fuzzy systems where interpretability of fuzzy systems is combined with the statistical properties of probabilistic systems. After having sketched the general architecture of TS probabilistic fuzzy systems, we present an appropriate mathematical framework and introduce two probabilistic fuzzy reasoning schemes which have a different interpretation but, eventually, yield the same input-output mapping. We illustrate our theoretical considerations by presenting some simulation results concerning a financial time series analysis.