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High order fuzzy time series forecasting methods are more suitable than first order fuzzy time series forecasting methods in dealing with linguistic values. However, existing high order methods lack persuasiveness in dealing objectively with multiple – factor fuzzy time series, recurrent number of fuzzy relationships, and assigning weights to elements of fuzzy forecasting rules. In this paper, a novel two – factor high – order fuzzy time series forecasting method based on fuzzy C-means clustering and particle swarm optimization is proposed to resolve these drawbacks. Fuzzy C-means clustering is utilized in the fuzzification phase to objectively partition the universe of discourse and enable processing of multiple factors. Then, particle swarm optimization is utilized to assign optimal weights to elements of fuzzy forecasting rules. Daily average temperatures of Taipei and Taiwan Futures Exchange (TAIFEX) are used as benchmark data. Average forecasting error performance of 0.85% was obtained for Taipei Temperature forecast. Mean squared error performance of 199.57 was obtained for Taiwan Futures Exchange forecast. The forecasting results showed that the proposed method has higher forecasting performance than other existing methods. Keywords: fuzzy time series, fuzzy c-mean clustering, particle swarm optimization, forecasting, fuzzy relationships

A novel two – factor high order fuzzy time series with applications to temperature and futures exchange forecasting