A new time series forecasting model based on the combination of intuitionistic fuzzy sets components

The forecasting of time series has a significant impact in our daily life, both theoretically and practically. Intutionistic fuzzy time series models, unlike fuzzy time series models, take into account the degree of hesitation of the observations, and they use memberships and non-membership values together as inputs in the forecasting system. To be able to reveal the membership and non-membership effects in the forecasting system, the membership and non-membership values need to be considered as separate inputs in the forecasting model. Moreover getting the outputs of the system by combining these separate models will provide both more accurate forecasts and a flexible approach. In the scope of this thesis, an intuitionistic fuzzy time series forecasting model (IFTS-PM) is proposed. Also for the determination of non-linear relations part a new hybrid sigma-pi neural network (HSP-NN) is used for the first time in the literature. Newly proposed HSP-NN multiples linear functions of inputs by unequal weights and converts them to nonlinear relationships. Two different HSP-NNs generate forecasts by considering the memberships and non-membership contributions separately. And final outputs are obtained by combining these outputs. To be able to obtain both optimal weights of HSP-NN s and combination weights modified particle swarm optimization is utulized. And, intuitionistic fuzzy C-means is performed to get fuzzy clusters, membership, and non-membership values. 15 implementations belong to TAIEX and IEX time series have been carried out in order to present the proposed models' performance. The results showed that the proposed model has superior forecasts compared to some other state-of-the-art forecasting tools in terms of different error criteria.