This article develops an alternative approach in modeling a hysteresis using Preisach model. A Preisach model is demonstrated geometrically by an inverted triangle, namely Preisach triangle, which contains an amount of fundamental operators. In a conventional Preisach model, these fundamental operators are ideal relays. Consequently, there exists an inherently discontinuous jump between two consecutive relays. To resolve this problem, in this work, a generalized linear operator is used as the fundamental elements. Correspondingly, its representative Preisach triangle consists of numerous discrete elements whose weight concentrates just along their diagonal. With such approach, it is possible to predict the response of the model according to any input without the aid of numerical interpolation tools. In addition, in this work, to determine the elements’ weights of the model, two accurate identification methods corresponding to two schemes of experimentally biased and unbiased dataset are developed. At last, several simulations and experiments are conducted to assess the effectiveness of the proposed approach showing comparative results with conventional Preisach model.