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Shear wave ultrasound elastography is a quantitative imaging approach in soft tissues based on viscosity-elastic properties. Complex shear modulus (CSM) estimation is an effective solution to analyze tissues' physical properties for elasticity and viscosity based on the wavenumber and attenuation coefficient. CSM offers a way to detect and classify some types of soft tissues. However, CSM-based elastography inherits some obstacles, such as estimation precision and calculation complexity. This work proposes an approach for two-dimensional CSM estimation and soft tissue classification using the Extended Kalman Filter (EKF) and Decision Tree (DT) algorithm, named the EKF-DT approach. CSM estimation is obtained by applying EKF to exploit shear wave propagation at each spatial point. Afterward, the classification of tissues is done by a direct and efficient decision tree algorithm categorizing three types of normal, cirrhosis, and fibrosis liver tissues. Numerical simulation scenarios have been employed to illustrate the recovered quality and practicality of the proposed method's liver tissue classification. With the EKF, the estimated wave number and attenuation coefficient are close to the ideal values, especially the estimated wave number. The states of three liver tissue types were automatically classified by applying the DT coupled with two proposed thresholds of elasticity and viscosity: (2.310 kPa, 1.885 Pa.s) and (3.620 kPa 3.146 Pa.s), respectively. The proposed method shows the feasibility of CSM estimation based on the wavenumber and attenuation coefficient by applying the EKF. Moreover, the DT can automate the classification of liver tissue conditions by proposing two thresholds. The proposed EKF-DT method can be developed by 3D image reconstruction and empirical data before applying it in medical practice.