A Fuzzy Similarity Measure for Fuzzy Time Series

With the capability of dealing with vague and incomplete data, the study of fuzzy time series has attracted great interest and is expected to expand rapidly. Song and Chissom (1993) first proposed the seven-step forecasting framework of fuzzy time series which are composed of (1) definition of the universe of discourse, (2) partitioning of the universe of discourse, (3) definition of fuzzy sets, (4) fuzzification of crisp time series, (5) construction of fuzzy logical relationships from the fuzzy time series, (6) forecasting, and (7) defuzzification of its output. A variety of forecasting models following Song and Chissom’s framework were subsequently proposed, most of them adopting IF-THEN rules for relationship representation and exact matching for forecasting step. Exact matching of fuzzy inferring in sparse fuzzy rule based, the question of selecting the suitable fuzzy similarity measure is necessary. The most common way of calculating similarity of fuzzy sets is based on the distance. Unfortunately, the similarity measure based on distance can not distinguish the relation degree of difference membership functions. In this research project, we attempt to propose a novel fuzzy similarity measure to suit forecasting step for fuzzy time series. We experimental results using a real-world data set and demonstrate that the proposed model outperforms the existing models in terms of accuracy.