F-transform; Fuzzy partition; Time series

The aim of this contribution is to show that the theory of F-transform can be successfully used in analysis and forecasting of time series. We propose relaxed constraints on a fuzzy partition as well as a matrix form of the F-transform for fast computation. For short time series, we propose to use the direct F-transform and make forecast on the basis of F-transform components. Most of the attention has been paid to the Mamdani-Assilian conjunctive kind of models of fuzzy rule bases built with help of particular t-norms. This paper focuses on the implicative approach for arbitrary residual implication.