A hybrid sigma-pi neural network for combined intuitionistic fuzzy time series prediction model

Intuitionistic fuzzy time series models consider observations hesitation degree but they use memberships and non-membership values together as inputs in the prediction system. The usage of membership and non-membership values as inputs in separate prediction models and combining the outputs of these separate models will provide a more flexible computational approach. Thus, different effects of membership and non-membership degrees on the predictions can be revealed. In this paper, an intuitionistic fuzzy time series prediction model (IFTS-PM) has been proposed. The proposed IFTS-PM uses a new hybrid sigma-pi neural network (HSP-NN), introduced for the first time in the literature, to determine nonlinear relationships between inputs and outputs. In addition, this newly proposed HSP-NN has the ability to multiply linear functions of inputs by unequal weights and convert them to nonlinear relationships. The structure of the proposed IFTS-PM consists of three parts. Two different HSP-NNs generate predictions by taking into account the different contribution levels of memberships and non-memberships. The last part is the part where these predictions are combined. Modified particle swarm optimization is performed to obtain optimal weights of HSP-NNs as well as the combination weights. And by taking the advantage of intuitionistic fuzzy C-means, fuzzy clusters, membership and non-membership values of observations are obtained. Performance of the proposed model is verified by applying it on 48 time series data sets. With all used indications, it has been clearly observed that proposed model has produced outstanding predictions compared to some other state-of-the-art prediction tools.