Consensus reaching process is an influential feature of social influence network theory and group decision making. The influence model undertakes a pivotal role where group decision making is based on opinion dynamics. Interpersonal influences of experts have an exceptional part of the influence model which is a dominant addition in social influence networks. Influence based model is a simple and satisfactory mathematical representation of the change of opinions due to the experts, influences. Uncertainty is presupposed in almost every direction of decision making and opinion dynamics so should also be included in the influence model. In this paper, the influence model is refined by utilizing the triangular fuzzy numbers in place of crisp numbers, where not only the initial opinions but also the interpersonal influences are represented as fuzzy numbers. This extends the influence model from ordinary numbers to fuzzy numbers. A fuzzy inverse matrix is computed by using a system of linear equations where coefficients and constants are fuzzy numbers. These equations are called fuzzy linear equations.