A Three-Domain Fuzzy Wavelet System for Simultaneous Processing of Time-Frequency Information and Fuzziness

Traditional wavelet system is a two-domain (time and frequency domains) wavelet system (2DWS), which works only in time and frequency domains. The 2DWS is not able to treat time-frequency information and fuzziness simultaneously. For this reason, a three-domain (fuzzy, time, and frequency domains) fuzzy wavelet system (3DFWS) is proposed, where the three-domain mechanism provides a solution to handle fuzzy uncertainties and time-frequency information together. The major advantage of 3DFWS is able to use the prior knowledge via the novel fuzzy domain to analyze uncertain data and signals, which will enhance the potentials of 2DWS. Experimental and simulation studies show that the performance of the proposed 3DFWS is superior to the traditional one for simultaneous processing of time-frequency and fuzziness.