Time Series Forecasting with New Type-2 Fuzzy T-Norms and T-Conorms

This paper presents new families of triangular norms and conorms specifically constructed for type-2 fuzzy sets. Our approach considers several partially ordered sets of membership functions defined on the unit interval, each characterized by different structural properties and suited to representing particular kinds of uncertainty. For these settings, we define operators that consistently represent fuzzy intersection and union, filling gaps where no such type-2 operators were previously available. It is the first time that triangular norms and conorms are obtained with respect to both usual partial orders in the set of normal membership functions. Building on this framework, we integrate the proposed operators into a type-2 fuzzy time series. A large-scale evaluation on multiple benchmark time series shows that the new operators consistently achieve the best predictive accuracy, in terms of MAPE, in comparison with classical type-2 and type-1 fuzzy time series baselines. These results demonstrate that the algebraic design of type-2 operators has a direct impact on forecasting performance and can substantially improve the modeling of uncertainty in time-dependent data.