Conventional time series forecast models can hardly develop the inherent rules of complex non-linear dynamic systems because the strict assumptions they need cannot always be met in reality, whereas fuzzy time series (FTS) techniques can be used even the records of times series have uncertainty and instability since they do not need strict assumptions. In previous study of FTS, the process of aggregating the past observations and assigning proper weights of fuzzy logical relationship groups are ignored, which may lead to poor forecasting accuracy since they are important aspects in time series prediction and analysis where determination of future trends depends only on past observations. In this paper, a novel high-order FTS model is constructed to make time series forecasting. Specifically, by applying the harmony search intelligence algorithm, the optimal lengths of intervals are tuned. Moreover, regularly increasing monotonic quantifiers are employed on fuzzy sets to obtain the weights of ordered weighted aggregation. Simultaneously, the weights of right-hand side of fuzzy logical relationship groups are explored to compensate the presence of bias in the prediction. In the part of empirical analysis, the developed model was applied to predict three well-known time series: numbers of enrollment of Alabama University, TAIEX and electricity load demand of New South Wales and the results obtained were compared with several counterparts, including some old and recently developed models. Experimental results demonstrate that the developed model cannot only achieve higher accuracy of prediction, but also capture the fuzzy features and characters.