In this study, a satisfaction index estimation model is proposed integrating structural equation modeling and mathematical programming methods with fuzzy customer data. Firstly, a deep literature survey is conducted in this field of study. Then, a new model is proposed by taking into consideration gaps in the literature. The estimation model is composed of five stages and first stage is building conceptual model in which measurement and latent variables are introduced. At the second stage, a fuzzy evaluation method is developed for decreasing subjectivity in customer data. At the third stage, for measurement variables that are directly observed, a measurement model is developed with Linear Structural Relations. In the solution of the measurement model maximum likelihood algorithm is used. In the solution of structural model that is composed of latent variables that are not directly observed, a mathematical estimation model is developed in this study at the fourth stage. Mathematical model is coded in ILOG Cplex Optimization Studio. In the mathematical model that minimizes estimation errors, structural relations and measurement variable weights (precedence coefficients) are defined as constraints. At the fifth and last stage, index scores are calculated with mathematical model outputs. Application of the model is carried out in public sector at a local government service point. In the application model, service quality, innovation, communication, satisfaction and cost perception dimensions are used. Application results are discussed for both measurement and latent variables in detail. The results of model we developed are also compared with an alternative model outcomes and we show that we achieve optimum estimation capability with minimum estimation errors.