A novel forecasting model based on the raised ordered pair fuzzy time series and fuzzy implication

In fuzzy time series (FTS) based forecasting models, FTS is utilized to depict the characteristic of time series. In the constructed FTS of the existing models, each moment consists of a fuzzy set to reflect the size range of data and aligns with people's semantic description. However, this FTS ignores some essential fuzzy information, for example the membership degree of data to fuzzy set, and then it fails to describe the feature of time series accurately and limits forecasting performance. To address these issues, ordered pair FTS is proposed in this study. This FTS is consisted of ordered pairs, including two aspects: the fuzzified fuzzy set of data and corresponding membership degree. Worth noting that the ordered pair FTS not only captures the characteristic of data accurately by making use of the information of fuzzy set, but also maintains its interpretability. Following this, ordered pair fuzzy logical relationship (FLR) is derived from antecedent ordered pair(s) to a consequent ordered pair, it describes the association of time series effectively through capturing data information exactly. Based on the ordered pair FLR, a forecasting model is designed. This model applies fuzzy implication to measure the truth degree of FLR and indicate the importance of each fuzzy rule in prediction, ultimately produces reasonable prediction result. The superiorities of the proposed ordered pair FTS and forecasting model are demonstrated in experimental studies, where they are compared with other existing forecasting models.