A single fuzzy rule to smooth the sharpness of mixed data: Time and frequency domains analysis

An essential part of any scientific study on any time series analysis depends strongly on availability of reliable data. It is a fact that experimental data records are always contaminated by inaccurate information, not only due to measurement errors but also due to ambiguity of measuring concepts. This occurs especially in fields related to the human science, where unexpected sharp signals are observed. However, due to lack of admissible error descriptions, fuzzy smoothing methods can be potentially considered as proper candidates for data processing. This paper presents a novel procedure based on a single fuzzy rule for smoothing out the sharpness of data curves which have mixed sample values. It further analyzes performance of the proposed method experimentally by focusing on both time domain properties and power spectrums. The proposed fuzzy smoothing filter checks for coarseness of the signal and then performs fine tunings of sharp points found in the signal by sharing their values with their neighboring points. A survey of both time and frequency domain performance reveals the superiority of the proposed method compared to other classical smoothing methods cited in the literature. Some applications are presented to better highlight the merit of the proposed method.