Signal Processing Using Fuzzy Fractal Dimension and Grade of Fractality -Application to Fluctuations in Seawater Temperature

摘要

Discrete signal processing using fuzzy fractal dimension and grade of fractality is proposed based on the novel concept of merging fuzzy theory and fractal theory. The fuzzy concept of fractality, or self-similarity, in discrete time series can be reconstructed as a fuzzy-attribution, i.e., a kind of fuzzy set. The objective short time series can be interpreted as an objective vector, which can be used by a newly proposed membership function. Sliding measurement using the local fuzzy fractal dimension (LFFD) and the local grade of fractality (LGF) is proposed and applied to fluctuations in seawater temperature around the Izu peninsula of Japan. Several remarkable characteristics are revealed through "fuzzy signal processing" using LFFD and LGF